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.
Thursday, December 17, 2009
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
Thursday, December 03, 2009
Geometry: 3-1 & 3-2 (Thursday)
Parallel Lines, Transversals, and their Angles
1. Read 3-1
2. Go to Google Earth, and zoom in on the Caribbean (southeast of the United States). Blackbeard normally trades along the route from Kingston (in modern Jamaica) to Port-au-Prince (modern Haiti), but raids and plunders along the route from the pirate haven of Tortuga (just north of Port-au-Prince) to the pirate haven of Port Royal (just north of Kingston).
The route that the Spanish armada patrols runs from Spain through these two routes, threatening Blackbeard each time. Could the terms transversal, or parallel, or skew lines be applied to these routes? If yes, which routes? If not, why not?
3. In 3-1, work problems 2, 4, 10-16 even (see example 2 & 3), 46-50 even, 53, 54, and 60
4. Read 3-2
5. In 3-2, work problems 4-10 even, 32, 34, and 42
Extra Credit: 3-2 #26-30 even, 36, and 48
1. Read 3-1
2. Go to Google Earth, and zoom in on the Caribbean (southeast of the United States). Blackbeard normally trades along the route from Kingston (in modern Jamaica) to Port-au-Prince (modern Haiti), but raids and plunders along the route from the pirate haven of Tortuga (just north of Port-au-Prince) to the pirate haven of Port Royal (just north of Kingston).
The route that the Spanish armada patrols runs from Spain through these two routes, threatening Blackbeard each time. Could the terms transversal, or parallel, or skew lines be applied to these routes? If yes, which routes? If not, why not?
3. In 3-1, work problems 2, 4, 10-16 even (see example 2 & 3), 46-50 even, 53, 54, and 60
4. Read 3-2
5. In 3-2, work problems 4-10 even, 32, 34, and 42
Extra Credit: 3-2 #26-30 even, 36, and 48
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