Angles of Elevation and Depression
Read 7-5 – this is just further application of SOH-CAH-TOA. Final Test in 2 days!
The alchemist sees Sally lurking outside his shop, and after a brief chat, hires her on as a servant. Today, she must fetch sulfur from the inland cliffs. After a half a day's trek, she reaches a cliff edge that looks down on broken rock dotted with yellow sulfur. If the cliff is 200 feet from the sulfur rocks, and the angle of depression is around 10 degrees, about how high is the cliff edge?
In 7-5, work problems 4-20 even, 28-44 even. Finally, go outside and find the height of the apartments next door! You'll need to find the angle from your eye to the building - talk to me to get help with the Angle of Elevation Device.
Extra Credit: # 19, 21-25 all. (21 is hard – you may need to draw a picture AND write an equation)
Showing posts with label geometry. Show all posts
Showing posts with label geometry. Show all posts
Monday, January 18, 2010
Friday, January 15, 2010
Geometry: 7-4 (Friday)
Trigonometry!
Read 7-4 – Now we can find every part of any right triangle, but the ratios are extremely difficult to memorize! Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. Look at the Key Concept and Example 1 until you get the basic idea, and then write SOH-CAH-TOA or some other reminder in your notes. Say it to yourself a few times to start memorizing it. You'll use this one a lot.
As the sun creeps into the cellar entrance, Sally wakes up and goes wandering through town. She comes across an alchemist, and likes the look of their sign. The “A” is a right triangle 16 inches high and 4 inches wide. What is the measure of the angle at the top? What is the length of the hypotenuse?
In 7-4, work problems 6-16 even, 17, 32-46 even, 49-52 ALL, 70-82 even.
Extra Credit: # 59-61 all, 66, and the following:
Refer to #59. A second is a very small angle measurement equal to 1/60th of a minute, which is equal to 1/60th of a degree. A parsec is a parallax second, in other words the distance from Earth an object would have to be to have a stellar parallax of 1 second, or 1/(60*60) = 1/3600 degree. How many astronomical units are there in a parsec? If NASA scientists find alien life 197 parsecs away on Betelgeuse, how many astronomical units is that?
Read 7-4 – Now we can find every part of any right triangle, but the ratios are extremely difficult to memorize! Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. Look at the Key Concept and Example 1 until you get the basic idea, and then write SOH-CAH-TOA or some other reminder in your notes. Say it to yourself a few times to start memorizing it. You'll use this one a lot.
As the sun creeps into the cellar entrance, Sally wakes up and goes wandering through town. She comes across an alchemist, and likes the look of their sign. The “A” is a right triangle 16 inches high and 4 inches wide. What is the measure of the angle at the top? What is the length of the hypotenuse?
In 7-4, work problems 6-16 even, 17, 32-46 even, 49-52 ALL, 70-82 even.
Extra Credit: # 59-61 all, 66, and the following:
Refer to #59. A second is a very small angle measurement equal to 1/60th of a minute, which is equal to 1/60th of a degree. A parsec is a parallax second, in other words the distance from Earth an object would have to be to have a stellar parallax of 1 second, or 1/(60*60) = 1/3600 degree. How many astronomical units are there in a parsec? If NASA scientists find alien life 197 parsecs away on Betelgeuse, how many astronomical units is that?
Thursday, January 14, 2010
Geometry: 7-2 and 7-3 (Thursday)
Special Properties of Right Triangles
Today is the last 2-section day!
1. Read 7-2: We can now use the converse of the Pythagorean Theorem! Feel your powers increase tenfold!
2. Sally can't sleep, so she wanders aimlessly through the dark town. One area seems to have been burnt by fire, and a wall, surrounded by charred wood and threatening to collapse, has been propped up by a beam. The beam is 9 feet long, and touches the wall 5 feet up and the ground 7 feet out. Is the wall standing upright?
3. In 7-2, work problems 6-12 even, 20, 28, 40, 52, 60, and 62.
4. Read 7-3: Two special right triangles with specific leg-leg-hypotenuse ratios.
Sally wanders around the collapsed house, and finds the stairs down to the cellar. A support has collapsed diagonally across the 3 foot wide cellar entrance. She finds cheeses and salted meat inside, eats, and falls asleep. If the collapsed entrance is a 30-60-90 triangle, how tall is it?
5. In 7-3, work problems 8-12 even, 18-22 even (draw 20 & 22!), 32, 40, 52, 54.
Extra Credit: In 7-2 # 36, 37, 42. In 7-3, # 24-28 even.
Today is the last 2-section day!
1. Read 7-2: We can now use the converse of the Pythagorean Theorem! Feel your powers increase tenfold!
2. Sally can't sleep, so she wanders aimlessly through the dark town. One area seems to have been burnt by fire, and a wall, surrounded by charred wood and threatening to collapse, has been propped up by a beam. The beam is 9 feet long, and touches the wall 5 feet up and the ground 7 feet out. Is the wall standing upright?
3. In 7-2, work problems 6-12 even, 20, 28, 40, 52, 60, and 62.
4. Read 7-3: Two special right triangles with specific leg-leg-hypotenuse ratios.
Sally wanders around the collapsed house, and finds the stairs down to the cellar. A support has collapsed diagonally across the 3 foot wide cellar entrance. She finds cheeses and salted meat inside, eats, and falls asleep. If the collapsed entrance is a 30-60-90 triangle, how tall is it?
5. In 7-3, work problems 8-12 even, 18-22 even (draw 20 & 22!), 32, 40, 52, 54.
Extra Credit: In 7-2 # 36, 37, 42. In 7-3, # 24-28 even.
Wednesday, January 13, 2010
Geometry: 7-1 (Wednesday)
First, take the Chapter 6 Quiz! If you need a few minutes to study, we can take some time to do that.
Read 7-1: Geometric means can be written as proportions, or as square roots. Make sure you understand both! This section can be confusing - ask me if it's not clear!
Unable to find food, Sally tries to sleep in the stable again, and ponders the roof (a right triangle with the right angle at the top), with its single vertical support (an altitude). If the roof is 13 feet wide, with 9 feet on one side of the support and 4 feet on the other side, how tall is the support?
In 7-1, work problems 6-12 even (for 12, draw it – this is ONE triangle, you just need to move the altitude), 36, 38, 42, 43, 50, 58-66 even. Finally, do the activity on p. 349 and answer questions 1-3 (yes, that means you'll do the activity twice – you can draw squares on your assignment paper, or get a separate sheet – ask me for a ruler if you need one)
Extra Credit # 28, 33, 34, 44, 45 (draw this out with a specific triangle, and remember the rules for similarity)
Read 7-1: Geometric means can be written as proportions, or as square roots. Make sure you understand both! This section can be confusing - ask me if it's not clear!
Unable to find food, Sally tries to sleep in the stable again, and ponders the roof (a right triangle with the right angle at the top), with its single vertical support (an altitude). If the roof is 13 feet wide, with 9 feet on one side of the support and 4 feet on the other side, how tall is the support?
In 7-1, work problems 6-12 even (for 12, draw it – this is ONE triangle, you just need to move the altitude), 36, 38, 42, 43, 50, 58-66 even. Finally, do the activity on p. 349 and answer questions 1-3 (yes, that means you'll do the activity twice – you can draw squares on your assignment paper, or get a separate sheet – ask me for a ruler if you need one)
Extra Credit # 28, 33, 34, 44, 45 (draw this out with a specific triangle, and remember the rules for similarity)
Tuesday, January 12, 2010
Geometry: 6-5 (Tuesday)
Today we're looking at more proportions between similar triangles. We'll have a quiz tomorrow, so keep those notes up to date and study tonight!
Read 6-5
After waking, Sally remembers she's in a strange town, in a stable. The roof of the stable is shaped the same as the roof of the inn next door. It has a short, steep side, and a long, shallow side. A vertical beam runs from the bottom to the top of each roof. If the stable's roof is 10 feet wide with a 6 foot beam, and the inn's roof is 25 feet wide, how tall is the inn's beam?
In 6-5, work problems 2-6 even, 12-18 even, 24-28 even, 34, and 40-46 even.
Extra Credit p. 324 # 1-5 – Sirpenski Triangles, an introduction to Fractals (you don't need to draw the triangles, if you can calculate in your head)
If you have time, check out these 3D fractals.
http://skytopia.com/project/fractal/mandelbulb.html
Additional Extra Credit: I'm planning on skipping Fractals. However, anyone interested may do 6-6 #4, 7-13 all, and 42 for a half an assignment's worth of extra credit.
FINALLY, if you do 6-6 first, you can also turn in a full-page fractal of your design (something iterative, at least mostly self-similar, and school appropriate) for another 5 points. It should include at least 5 stages.
Read 6-5
After waking, Sally remembers she's in a strange town, in a stable. The roof of the stable is shaped the same as the roof of the inn next door. It has a short, steep side, and a long, shallow side. A vertical beam runs from the bottom to the top of each roof. If the stable's roof is 10 feet wide with a 6 foot beam, and the inn's roof is 25 feet wide, how tall is the inn's beam?
In 6-5, work problems 2-6 even, 12-18 even, 24-28 even, 34, and 40-46 even.
Extra Credit p. 324 # 1-5 – Sirpenski Triangles, an introduction to Fractals (you don't need to draw the triangles, if you can calculate in your head)
If you have time, check out these 3D fractals.
http://skytopia.com/project/fractal/mandelbulb.html
Additional Extra Credit: I'm planning on skipping Fractals. However, anyone interested may do 6-6 #4, 7-13 all, and 42 for a half an assignment's worth of extra credit.
FINALLY, if you do 6-6 first, you can also turn in a full-page fractal of your design (something iterative, at least mostly self-similar, and school appropriate) for another 5 points. It should include at least 5 stages.
Monday, January 11, 2010
Geometry: 6-4 (Monday)
Today is Parallels and Proportions!
Read 6-4 – Now we can cut triangles into proportional sections! Tomorrow we'll look at more parts of triangles, and then Wednesday we'll have a quiz over all of Ch. 6.
As Blackbeard's flotilla resupplies at Santo Domingo, on the island of Hispaniola, Gunnel Sally slips out into town. By the time she returns, the ships are gone! She sleeps in a stable, and has a terrible dream. A giant is running after her! Its right leg is longer than the left and swings out sideways, but both of its knees brush the rooftops as it runs after her. When she wakes up, she finds comfort in triangles and proportions. What can be said about the monster's lower and upper legs?
In 6-4, work problems 4-16 even, 20-24 even, 28, 46-60 even.
Extra Credit # 18, 26, 35-37
Read 6-4 – Now we can cut triangles into proportional sections! Tomorrow we'll look at more parts of triangles, and then Wednesday we'll have a quiz over all of Ch. 6.
As Blackbeard's flotilla resupplies at Santo Domingo, on the island of Hispaniola, Gunnel Sally slips out into town. By the time she returns, the ships are gone! She sleeps in a stable, and has a terrible dream. A giant is running after her! Its right leg is longer than the left and swings out sideways, but both of its knees brush the rooftops as it runs after her. When she wakes up, she finds comfort in triangles and proportions. What can be said about the monster's lower and upper legs?
In 6-4, work problems 4-16 even, 20-24 even, 28, 46-60 even.
Extra Credit # 18, 26, 35-37
Friday, January 08, 2010
Geometry: 6-3 (Friday)
Similar Triangles
Read 6-3 – Keep your binder up to date with these theorems! VERY similar to the congruence theorems, but instead of ASA and AAS we simply have AA – any two congruent angles makes it similar!
The mainmast on Gunnel Sally's ship is topped by a triangular sail. A reefline cuts across it, and that line is exactly parallel to the base of the triangle. Is the triangular top section of the sail similar to the whole triangular sail? Why or why not?
In 6-3 work problems 2-10 even, 20, 26-32 even (on 28, start by looking for more right angles and parallel lines), 36, 40, and 50-60 even.
Extra Credit # 41, 42 (think about the city context), 45, and 46.
Read 6-3 – Keep your binder up to date with these theorems! VERY similar to the congruence theorems, but instead of ASA and AAS we simply have AA – any two congruent angles makes it similar!
The mainmast on Gunnel Sally's ship is topped by a triangular sail. A reefline cuts across it, and that line is exactly parallel to the base of the triangle. Is the triangular top section of the sail similar to the whole triangular sail? Why or why not?
In 6-3 work problems 2-10 even, 20, 26-32 even (on 28, start by looking for more right angles and parallel lines), 36, 40, and 50-60 even.
Extra Credit # 41, 42 (think about the city context), 45, and 46.
Thursday, January 07, 2010
Geometry: 6-1 and 6-2 (Thursday)
Take the Chapter 5 Quiz!
6-1 and 6-2: Proportions and Similarity
1. Read 6-1 – ratios are simply another way of writing fractions.
2. Blackbeard comes across a merchant fleet. This fleet is heavily armed, with 500 cannons among its ships. Blackbeard's ships only boast 300 cannons. What is the ratio of Blackbeard's cannons to the merchants' cannons?
3. In 6-1 work problems 2, 4, 16, 26 (look back at proportions), 40, 44, 46.
4. Gunnel Sally enjoys poking around the captain's cabin while he's not there. Her favorite object is a scale model of the ship. If it's a perfect reproduction, and a 50 foot tall mast is 10 inches on the model, how wide would the captain's cabin be, if it's 10 feet wide in real life?
5. Read 6-2 – we'll use ratios to see if two polygons are similar.
6. In 6-2 work problems 4-8 even, 28, 32, 36, 52, 62, and 73.
Extra Credit: 6-1 # 23-25. 6-2 # 16, 26, and 44.
6-1 and 6-2: Proportions and Similarity
1. Read 6-1 – ratios are simply another way of writing fractions.
2. Blackbeard comes across a merchant fleet. This fleet is heavily armed, with 500 cannons among its ships. Blackbeard's ships only boast 300 cannons. What is the ratio of Blackbeard's cannons to the merchants' cannons?
3. In 6-1 work problems 2, 4, 16, 26 (look back at proportions), 40, 44, 46.
4. Gunnel Sally enjoys poking around the captain's cabin while he's not there. Her favorite object is a scale model of the ship. If it's a perfect reproduction, and a 50 foot tall mast is 10 inches on the model, how wide would the captain's cabin be, if it's 10 feet wide in real life?
5. Read 6-2 – we'll use ratios to see if two polygons are similar.
6. In 6-2 work problems 4-8 even, 28, 32, 36, 52, 62, and 73.
Extra Credit: 6-1 # 23-25. 6-2 # 16, 26, and 44.
Tuesday, January 05, 2010
Geometry: 5-4 and 5-5 (Tuesday)
Triangle Inequalities
Spock: "But Mister Kemp, we aren't finished with yesterday's assignment. Now we're supposed to do a double-assignment today, too?"
Mister Kemp: "I know. Trust me, it'll be okay. Tomorrow we'll have some time to finish it all up."
Spock: "Yay! I'm going to get on Farmville and-"
Mister Kemp: "THAT BEING SAID, the Chapter 5 quiz will be first thing on Thursday, and you will need to be ready for it! And these last two assignments are slightly longer than usual. Use your time wisely!"
1. Blackbeard takes his fleet from Maracaibo up to Kingston, and then heads for Nassau in The Bahamas. If the trip to Kingston is 500 miles, and from there to Nassau is another 600 miles, what's the furthest it could possibly be from Maracaibo directly to Nassau?
2. Read 5-4 – Keep track of these theorems in your binder! Make sure you understand the concepts before moving on to the problems! Get my help if you need it.
3. In 5-4, work problems 2-10 even, 44, 52.
4. Read 5-5
5. The cannons on the new ship can be raised to aim higher in the air. Gunnel Sally notices two cannons next to each other, the first raised to a high angle and the second cannon at a very low angle, almost parallel to the deck. Which cannon's mouth will be farther from the deck, and which theorem proves this?
6. In 5-5, work problems 4, 6, 12-16 even.
Extra Credit: 5-4 # 34, 36, and 46. 5-5 # 8, 9, 28, and 30.
Spock: "But Mister Kemp, we aren't finished with yesterday's assignment. Now we're supposed to do a double-assignment today, too?"
Mister Kemp: "I know. Trust me, it'll be okay. Tomorrow we'll have some time to finish it all up."
Spock: "Yay! I'm going to get on Farmville and-"
Mister Kemp: "THAT BEING SAID, the Chapter 5 quiz will be first thing on Thursday, and you will need to be ready for it! And these last two assignments are slightly longer than usual. Use your time wisely!"
1. Blackbeard takes his fleet from Maracaibo up to Kingston, and then heads for Nassau in The Bahamas. If the trip to Kingston is 500 miles, and from there to Nassau is another 600 miles, what's the furthest it could possibly be from Maracaibo directly to Nassau?
2. Read 5-4 – Keep track of these theorems in your binder! Make sure you understand the concepts before moving on to the problems! Get my help if you need it.
3. In 5-4, work problems 2-10 even, 44, 52.
4. Read 5-5
5. The cannons on the new ship can be raised to aim higher in the air. Gunnel Sally notices two cannons next to each other, the first raised to a high angle and the second cannon at a very low angle, almost parallel to the deck. Which cannon's mouth will be farther from the deck, and which theorem proves this?
6. In 5-5, work problems 4, 6, 12-16 even.
Extra Credit: 5-4 # 34, 36, and 46. 5-5 # 8, 9, 28, and 30.
Monday, January 04, 2010
Geometry: 5-3 (Monday)
Review and Indirect Proofs
In 5-1, work problems 14, 23, and 26. Make sure to show your work!
In 5-2, work problems 20, 30, 42, and 48. Show all your work here, too!
Read 5-3
In several instances, the entire universe has almost been destroyed, but in each case Spock stepped in to save everything. Using indirect reasoning and this fact, write a short informal proof that the universe needs Spock to exist (i.e. for the universe to exist, Spock must exist).
The 5-3 problems are mostly small - just remember, I tend to pick the big ones to grade: In 5-3, work problems 4-8 even, 14-18 even, 22, 24, 38, 42-48 even.
Extra Credit: # 12, 31, 36, 40 (on #40 you'll need to prove the two halves are congruent).
In 5-1, work problems 14, 23, and 26. Make sure to show your work!
In 5-2, work problems 20, 30, 42, and 48. Show all your work here, too!
Read 5-3
In several instances, the entire universe has almost been destroyed, but in each case Spock stepped in to save everything. Using indirect reasoning and this fact, write a short informal proof that the universe needs Spock to exist (i.e. for the universe to exist, Spock must exist).
The 5-3 problems are mostly small - just remember, I tend to pick the big ones to grade: In 5-3, work problems 4-8 even, 14-18 even, 22, 24, 38, 42-48 even.
Extra Credit: # 12, 31, 36, 40 (on #40 you'll need to prove the two halves are congruent).
Thursday, December 17, 2009
Geometry: 5-2 (Thursday)
Inequalities and Triangles - Remember to study for the test tomorrow! Also, the last few assignments are due at that time, finish them up tonight if you want full credit for them.
1. Read 5-2
2. Gunnel Sally likes hanging out under the shade of the mizzensail after her shift of watch atop the high crow's nest, because there are fewer people at the back of the ship. Mostly just the captain and officers, who ignore her. One of the exterior angles of the triangular mizzensail measures 130 degrees. What interior angles is this angle definitely larger than? Justify your answer.
3. In 5-2, work problems 4-14 even, 22-26 even (remember angles that are part of another angle are by definition smaller than it), 32-40 even, 45, 56, 62-68 even.
Extra Credit: # 1, 16, 28, 46, 57, 58.
1. Read 5-2
2. Gunnel Sally likes hanging out under the shade of the mizzensail after her shift of watch atop the high crow's nest, because there are fewer people at the back of the ship. Mostly just the captain and officers, who ignore her. One of the exterior angles of the triangular mizzensail measures 130 degrees. What interior angles is this angle definitely larger than? Justify your answer.
3. In 5-2, work problems 4-14 even, 22-26 even (remember angles that are part of another angle are by definition smaller than it), 32-40 even, 45, 56, 62-68 even.
Extra Credit: # 1, 16, 28, 46, 57, 58.
Wednesday, December 16, 2009
Geometry: 5-1 (Wednesday)
Bisectors, Medians, and Altitudes - This and 5-2 will be on the test, keep updating your notes!
1. Read 5-1
2. The smells accompanying the captivity of over a hundred human beings are slowly washing out of the lower deck. One of the freed slaves, nicknamed Gunnel Sally by the ship's newly appointed captain, contemplates the triangular mizzensail. Three ropes run from its corners to a point near its center. After careful observation, Gunnel Sally notices that the ropes are all the same length. What is the name of their meeting point?
3. In 5-1, work problems 2-10 even (hint for 6: look at what you've learned about perpendicular bisectors. hint for 10: you will need to show that triangles EAD and EBD are congruent), 16-24 even, 34-38 ALL, 42, 46-54 even.
Extra Credit: # 14, 26-30 all.
1. Read 5-1
2. The smells accompanying the captivity of over a hundred human beings are slowly washing out of the lower deck. One of the freed slaves, nicknamed Gunnel Sally by the ship's newly appointed captain, contemplates the triangular mizzensail. Three ropes run from its corners to a point near its center. After careful observation, Gunnel Sally notices that the ropes are all the same length. What is the name of their meeting point?
3. In 5-1, work problems 2-10 even (hint for 6: look at what you've learned about perpendicular bisectors. hint for 10: you will need to show that triangles EAD and EBD are congruent), 16-24 even, 34-38 ALL, 42, 46-54 even.
Extra Credit: # 14, 26-30 all.
Tuesday, December 15, 2009
Geometry: 4-6 (Tuesday)
Isosceles Triangles Today! Take a second and see if you can remember the difference between Isosceles and Equilateral.
1. Open up Blackbeard's newly captured slave ship again in Sketchup. If the mizzensail (rear sail) is an isosceles triangle, then what can be said of the legs (the two long sides)? What can be said of the base angles (the two angles toward the back of the ship)?
2. Read 4-6
3. In 4-6, work problems 2-28 even, 44, 50, 52.
Extra Credit: # 30 (first step – congruent triangles), 34, 36, 38, 42.
1. Open up Blackbeard's newly captured slave ship again in Sketchup. If the mizzensail (rear sail) is an isosceles triangle, then what can be said of the legs (the two long sides)? What can be said of the base angles (the two angles toward the back of the ship)?
2. Read 4-6
3. In 4-6, work problems 2-28 even, 44, 50, 52.
Extra Credit: # 30 (first step – congruent triangles), 34, 36, 38, 42.
Monday, December 14, 2009
Geometry: 4-5 (Monday)
ASA and AAS Congruence
1. Read 4-5, and fill out your repertoire of different kinds of triangle congruence. Get this stuff in your notes! SSS, SAS, AAS, and ASA, along with other postulates and theorems that we're using.
2. Blackbeard was beaten back by the Spanish ships guarding Maracaibo, but luck favors the bold! He catches a slave ship transporting their human cargo to that city, and the entire crew surrenders! He maroons them on the Spanish Main (the mainland) and many of the slaves join him in piracy. NOTE: This part is historically realistic, although his assault on Maracaibo is not.
He fills the hold with cannon at the nearest pirate haven, and sails off. Let's take a look at the new ship. Download the pirate ship here and take a look at it in SketchUp.
This ship has three triangular sails stretched between the mainmast and foremast. If the points at which they attached to the mainmast form angles of 40 degrees and 100 degrees, what third piece of information would prove the triangles congruent?
3. In 4-5, work problems 4, 8, 18, 22-28 even, 32-40 even
4. ALSO read p. 214 "Congruence in Right Triangles" and work problems 1-5 as the last part of your assignment
Extra Credit: #14, 19, 29, p. 214 Congruence in Right Triangles #8 & 10
1. Read 4-5, and fill out your repertoire of different kinds of triangle congruence. Get this stuff in your notes! SSS, SAS, AAS, and ASA, along with other postulates and theorems that we're using.
2. Blackbeard was beaten back by the Spanish ships guarding Maracaibo, but luck favors the bold! He catches a slave ship transporting their human cargo to that city, and the entire crew surrenders! He maroons them on the Spanish Main (the mainland) and many of the slaves join him in piracy. NOTE: This part is historically realistic, although his assault on Maracaibo is not.
He fills the hold with cannon at the nearest pirate haven, and sails off. Let's take a look at the new ship. Download the pirate ship here and take a look at it in SketchUp.
This ship has three triangular sails stretched between the mainmast and foremast. If the points at which they attached to the mainmast form angles of 40 degrees and 100 degrees, what third piece of information would prove the triangles congruent?
3. In 4-5, work problems 4, 8, 18, 22-28 even, 32-40 even
4. ALSO read p. 214 "Congruence in Right Triangles" and work problems 1-5 as the last part of your assignment
Extra Credit: #14, 19, 29, p. 214 Congruence in Right Triangles #8 & 10
Friday, December 11, 2009
Geometry: 4-3, 4-4 (Friday)
More triangles! Today: Congruence, SSS and SAS Congruence
1. Read 4-3
2. In 4-3, work problems 4, 12, 20, 24, 30, 38
3. Read 4-4
4. Exploring the derelict vessel from last time, Spock finds a strange turbine, consisting of three blades. Each blade is a triangle with two long sides and a short side, and they're joined together at their smallest angle. If the long sides of each blade measure 1 meter and 1.5 meters, what other information would prove that all three blades are congruent?
5. In 4-4, work problems 2, 8, 9, 20-24 even, and 30.
Extra Credit: p. 199 Making Concept Maps 1-3, 4-4 problem 4, 9, and 19.
1. Read 4-3
2. In 4-3, work problems 4, 12, 20, 24, 30, 38
3. Read 4-4
4. Exploring the derelict vessel from last time, Spock finds a strange turbine, consisting of three blades. Each blade is a triangle with two long sides and a short side, and they're joined together at their smallest angle. If the long sides of each blade measure 1 meter and 1.5 meters, what other information would prove that all three blades are congruent?
5. In 4-4, work problems 2, 8, 9, 20-24 even, and 30.
Extra Credit: p. 199 Making Concept Maps 1-3, 4-4 problem 4, 9, and 19.
Wednesday, December 09, 2009
Geometry: 4-1 & 4-2 (Thursday)
Quiz Today!
Then on to Triangles:
1. Read 4-1
2. Betelgeuse, Bellatrix, and Rigel could be plotted at (-2, 5), (1,5), and (3,-3), respectively. These stars form a Bermuda triangle of the heavens (known as the Funkangulum), which Spock is the only organism to have entered and appeared outside again. What are TWO terms that apply to this triangle?
3. In 4-1, work problems 4, 7, 30, 44, 49.
4. Read 4-2
5. This time Spock is going to skirt around the Funkangulum. He travels from Betelgeuse to Bellatrix, and then turns toward Rigel. If the angle at Betelgeuse measures 40 degrees, and the angle at Rigel measures 20 degrees, how much did Spock turn at Bellatrix to head toward Rigel?
6. In 4-2, work problems 2-10 even, 36, 38, 48.
Extra Credit: 4-2 #12, 18-22 even, 45.
Then on to Triangles:
1. Read 4-1
2. Betelgeuse, Bellatrix, and Rigel could be plotted at (-2, 5), (1,5), and (3,-3), respectively. These stars form a Bermuda triangle of the heavens (known as the Funkangulum), which Spock is the only organism to have entered and appeared outside again. What are TWO terms that apply to this triangle?
3. In 4-1, work problems 4, 7, 30, 44, 49.
4. Read 4-2
5. This time Spock is going to skirt around the Funkangulum. He travels from Betelgeuse to Bellatrix, and then turns toward Rigel. If the angle at Betelgeuse measures 40 degrees, and the angle at Rigel measures 20 degrees, how much did Spock turn at Bellatrix to head toward Rigel?
6. In 4-2, work problems 2-10 even, 36, 38, 48.
Extra Credit: 4-2 #12, 18-22 even, 45.
Tuesday, December 08, 2009
Geometry: 3-6 (Wednesday)
Quiz tomorrow! The last couple assignments will be marked down after tomorrow, so get them in! You may want to talk to me about taking a book home.
Perpendiculars and Distance
1. Read 3-6
2. A derelict vessel is drifting toward a Vulcan mining station. Spock, having become aware of this danger, beams aboard the vessel, hacks the controls, and attempts to steer it away from the collision.
In the plane defined by the vessel's trajectory and the station, the vessel, starting at the origin (0,0) with a slope of ½, comes within mere meters of the station's fragile drill assembly, at (5,8). How close did it get?
3. In the book, work problems 2-14 even, 24, 34 - 44 even (draw 34!)
Extra Credit: Problems 18-22 even, 29, 30, 32.
Perpendiculars and Distance
1. Read 3-6
2. A derelict vessel is drifting toward a Vulcan mining station. Spock, having become aware of this danger, beams aboard the vessel, hacks the controls, and attempts to steer it away from the collision.
In the plane defined by the vessel's trajectory and the station, the vessel, starting at the origin (0,0) with a slope of ½, comes within mere meters of the station's fragile drill assembly, at (5,8). How close did it get?
3. In the book, work problems 2-14 even, 24, 34 - 44 even (draw 34!)
Extra Credit: Problems 18-22 even, 29, 30, 32.
Geometry: 3-5 (Tuesday)
How do you Prove that 2 Lines are Parallel?
1. Blackbeard's fleet of 7 assorted warships and refitted merchant ships arrives at Maracaibo, intent on a raid. However, the coast is protected by a line of Spanish war frigates, and behind them a fort wall with cannon poking out. Blackbeard approaches at a 45 degree angle to the line of ships. This also puts him at a 45 degree angle to the line of cannons. What is true about the two lines?
2. Read 3-5 and add a justification for what you said about the lines in part 1.
3. In the book, work problems 2-8 even, 16-20 even, 30, 34, 38, 40, 46-52 even, 64.
Extra Credit: Problems 10 (hint - start with postulate 3.4), 12, 22, 32, 36, and 42.
1. Blackbeard's fleet of 7 assorted warships and refitted merchant ships arrives at Maracaibo, intent on a raid. However, the coast is protected by a line of Spanish war frigates, and behind them a fort wall with cannon poking out. Blackbeard approaches at a 45 degree angle to the line of ships. This also puts him at a 45 degree angle to the line of cannons. What is true about the two lines?
2. Read 3-5 and add a justification for what you said about the lines in part 1.
3. In the book, work problems 2-8 even, 16-20 even, 30, 34, 38, 40, 46-52 even, 64.
Extra Credit: Problems 10 (hint - start with postulate 3.4), 12, 22, 32, 36, and 42.
Monday, December 07, 2009
Geometry: 3-4 (Monday)
Point-Slope Form and Slope-Intercept Form for Lines
1. Read 3-4
2. Captain Blackbeard's flagship has 65 hogsheads full of freshwater storage. If his crew consumes 2 hogsheads worth of water per day, write the equation for this consumption in slope-intercept form.
Head again to Google Earth and the Caribbean. Captain Henry Morgan sacked Maracaibo decades earlier, but Blackbeard thinks he can do it again. After filling his hogsheads full of freshwater in Santo Domingo, he sails south toward Maracaibo on the mainland. Using the coordinates of the two cities (to the nearest degree), find his course in point-slope form.
3. In the book, work problems 2-30 even, 36-42 even, 46, 47, 54-64, 69, and 70.
Extra Credit: Problems 31-33, 43, 44, 50-52, and the following:
If Blackbeard spots a merchant vessel ripe for plunderin', and sails off from Santo Domingo at a slope of -0.5 in search of it, where might he ultimately end up if he just keeps going? (pay attention to coordinates)
1. Read 3-4
2. Captain Blackbeard's flagship has 65 hogsheads full of freshwater storage. If his crew consumes 2 hogsheads worth of water per day, write the equation for this consumption in slope-intercept form.
Head again to Google Earth and the Caribbean. Captain Henry Morgan sacked Maracaibo decades earlier, but Blackbeard thinks he can do it again. After filling his hogsheads full of freshwater in Santo Domingo, he sails south toward Maracaibo on the mainland. Using the coordinates of the two cities (to the nearest degree), find his course in point-slope form.
3. In the book, work problems 2-30 even, 36-42 even, 46, 47, 54-64, 69, and 70.
Extra Credit: Problems 31-33, 43, 44, 50-52, and the following:
If Blackbeard spots a merchant vessel ripe for plunderin', and sails off from Santo Domingo at a slope of -0.5 in search of it, where might he ultimately end up if he just keeps going? (pay attention to coordinates)
Friday, December 04, 2009
Geometry: 3-3 (Friday)
Slopes of Lines
1. Read 3-3
2. Go to Google Earth and look southeast of the U.S. to the Caribbean again. Notice Kingston, in modern Jamaica, and Port-au-Prince, in modern Haiti. When Blackbeard sails his 7 free frigates from Kingston to Port-au-Prince, plundering merchant ships along the way, what is the slope of the line he makes? (note that at the bottom of the screen the latitude and longitude of your mouse is shown) When he flees from the Spanish Armada on the way back to Port-au-Prince from Kingston, what is the slope of that reverse course?
3. In 3-3, work problems 2-12 even, 16-22 even, 32-36 even, 40, 50-52 even, 56-60 even, 66-72 even
Extra Credit: Problems 24-30 even, 38, and 42-46 even
1. Read 3-3
2. Go to Google Earth and look southeast of the U.S. to the Caribbean again. Notice Kingston, in modern Jamaica, and Port-au-Prince, in modern Haiti. When Blackbeard sails his 7 free frigates from Kingston to Port-au-Prince, plundering merchant ships along the way, what is the slope of the line he makes? (note that at the bottom of the screen the latitude and longitude of your mouse is shown) When he flees from the Spanish Armada on the way back to Port-au-Prince from Kingston, what is the slope of that reverse course?
3. In 3-3, work problems 2-12 even, 16-22 even, 32-36 even, 40, 50-52 even, 56-60 even, 66-72 even
Extra Credit: Problems 24-30 even, 38, and 42-46 even
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