Look at the quiz here.
Friday, May 29, 2009
Wednesday, April 29, 2009
April 29th, 2009
1. Warm-up Read page 475 to 476
2. Do investigation 1 on page 475. Use geogebra or activestudio. Fill in the blank on conjecture 475: Isosceles Right Triangle Conjecture: In an isosceles right triangle, if the legs have length l, then the hypotenuse has length_______.
3. Do investigation 2 on page 476. Use geogebra or activestudio. Fill in the blank on the conjecture: 30-60-90 Triangle Conjecture: In a 30-60-90 triangle, if the shorter leg has length a, then the longer leg has length _____ and the hypotenuse has length _____.
4. Classwork 1 through 11, homework 12 and 13 page 478.
2. Do investigation 1 on page 475. Use geogebra or activestudio. Fill in the blank on conjecture 475: Isosceles Right Triangle Conjecture: In an isosceles right triangle, if the legs have length l, then the hypotenuse has length_______.
3. Do investigation 2 on page 476. Use geogebra or activestudio. Fill in the blank on the conjecture: 30-60-90 Triangle Conjecture: In a 30-60-90 triangle, if the shorter leg has length a, then the longer leg has length _____ and the hypotenuse has length _____.
4. Classwork 1 through 11, homework 12 and 13 page 478.
Monday, April 27, 2009
April 27th, 2009
1. Warm-up Read page 462 to 464. Talk to a partner, can you explain what the pythagorean theorem is?
2. Use activestudio to show evidence that the pythagorean theorem is true. Put a grid on the screen and make a right triangle with two sides with measures 6 and 8 or 9 and 12 or 5 and 12. Then, construct squares on each side. Then rotate the diagram and see that a^2 + b^2 = c^2.
Look at this video when you are finished.
3. Classwork 1 though 11 page 465.
Homework 12 to 16. If you need to, write these problems down. Otherwise, I'll post them here.
12. A basball infield is a square, each side measuring 90 feet. To the nearest foot, what is the distance from home plate to second base?
13. The diagonal of a square measures 32 meters. What is the area of the square?
14. What is the length of the diagonal of a square whose area is 64 cm squared?
15. The length of the three sides of a right triangle are consecutive integers. Find them.
16. A rectangular garden 6 meters wide has a diagonal measureing 10 meters. Find the perimeter of the garden.
2. Use activestudio to show evidence that the pythagorean theorem is true. Put a grid on the screen and make a right triangle with two sides with measures 6 and 8 or 9 and 12 or 5 and 12. Then, construct squares on each side. Then rotate the diagram and see that a^2 + b^2 = c^2.
Look at this video when you are finished.
3. Classwork 1 though 11 page 465.
Homework 12 to 16. If you need to, write these problems down. Otherwise, I'll post them here.
12. A basball infield is a square, each side measuring 90 feet. To the nearest foot, what is the distance from home plate to second base?
13. The diagonal of a square measures 32 meters. What is the area of the square?
14. What is the length of the diagonal of a square whose area is 64 cm squared?
15. The length of the three sides of a right triangle are consecutive integers. Find them.
16. A rectangular garden 6 meters wide has a diagonal measureing 10 meters. Find the perimeter of the garden.
Friday, April 24, 2009
Thursday, April 23, 2009
Friday, April 17, 2009
Monday, April 13, 2009
Monday, April 13th, 2009
1. Welcome back from Spring Break!
2. Please read 306 in the textbook to warm-up. Can you answer the questions? #1 is f.
3. Lots of investigations to do today. Work with a partner. Talk about geometry. Use geogebra to explore the concepts. We will share out as class progresses. It is very important to stay focused and work hard.
4. Investigation results:
Investigation 1 on page 307:
Define a central angle: A central angle has its vertex at the ____________________.
Define an inscribed angle: An inscribed angle has its vertex on the ___________________
and its sides are _____________.
Investigation 2 on page 307. Use geogebra. Carefully follow all the steps. Fill in the blank:
Chord central angles conjecture: If two chords in a circle are congruent, then they determine two central angles that are _____________.
Chord arcs conjecture: If two chords in a circle are congruent, then their _________________ are congruent.
Investigation 3 on page 309. Use geogebra. Fill in the blank:
Perpendicular to a chord conjecture: The perpendicular from the center of a circle to a chord is the ______________ of the chord.
Chord distance to center conjecture: Two congruent chords in a circle are ________________ from the center of the circle.
Investigation 4 on page 309. Use geogebra. Fill in the blank:
Perpendicular bisectors of a chord conjecture: The perpendicular bisector of a chord ___________________________________________.
5. Do question 1 through 9 on page 310 for homework.
2. Please read 306 in the textbook to warm-up. Can you answer the questions? #1 is f.
3. Lots of investigations to do today. Work with a partner. Talk about geometry. Use geogebra to explore the concepts. We will share out as class progresses. It is very important to stay focused and work hard.
4. Investigation results:
Investigation 1 on page 307:
Define a central angle: A central angle has its vertex at the ____________________.
Define an inscribed angle: An inscribed angle has its vertex on the ___________________
and its sides are _____________.
Investigation 2 on page 307. Use geogebra. Carefully follow all the steps. Fill in the blank:
Chord central angles conjecture: If two chords in a circle are congruent, then they determine two central angles that are _____________.
Chord arcs conjecture: If two chords in a circle are congruent, then their _________________ are congruent.
Investigation 3 on page 309. Use geogebra. Fill in the blank:
Perpendicular to a chord conjecture: The perpendicular from the center of a circle to a chord is the ______________ of the chord.
Chord distance to center conjecture: Two congruent chords in a circle are ________________ from the center of the circle.
Investigation 4 on page 309. Use geogebra. Fill in the blank:
Perpendicular bisectors of a chord conjecture: The perpendicular bisector of a chord ___________________________________________.
5. Do question 1 through 9 on page 310 for homework.
Thursday, April 2, 2009
Monday, March 30, 2009
Monday, March 30th, 2009
1. We need to wrap up chapter 5, so lets focus and work hard today.
2. Fill in the blank: Parallelogram opposite angles conjecture: The opposite angles of a parallelogram are _______________. In order to do this, construct a parallelogram on geogebra and measure the angles. See how to make a parallelogram video.
3. Fill in the blank: Parallelogram consecutive angles conjecture: The consecutive angles of a parallelogram are ___________________. (Remember that consecutive angles are next to each other.) Use the same parallelogram to figure this one out.
4. Fill in the blank: Parallelogram opposite sides conjecture: The opposite sides of a parallelogram are __________________. This time measure the length of the sides. Many of you should be able to figure this one out without even doing any work, the answer is obvious.
5. Fill in the blank: Parallelogram diagonals conjecture: The diagonals of a parallelogram __________________________________. Connect the opposite vertices with a diagonal and take measurements.
6. Fill in the blank: Double-edged straightedge conjecture: If two parallel lines are intersected by a second pair of parallel lines that are the same distance apart as the first pair, then the parallelogram formed is a _______________. See if you can create this on geogebra. The final answer is a not "square" however.
7. Fill in the blank: Rhombus diagonals conjecture: The diagonals of a rhombus are ___________________, and they ____________________________. Using a rhombus you've created on geogebra, connect the diagonals and measure angles and distances.
8. Fill in the blank: Rhombus angles conjecture: The _______________ of a rhombus ________________ the angles of the rhombus. Measure the angles.
9. Fill in the blank: Rectangle diagonals conjecture: The diagonals of a rectangle are _____________ and __________________. Make a rectangle, connect the opposite vertices, and measure angles and distances.
10. Fill in the blank: Square diagonals conjecture: The diagonals of a square are ______________, _______________ and ____________________. You should be able to figure this one out just by looking at all the work you've done to this point.
11. Homework: 1 through 6 on page 281, 1 through 11 on page 290.
2. Fill in the blank: Parallelogram opposite angles conjecture: The opposite angles of a parallelogram are _______________. In order to do this, construct a parallelogram on geogebra and measure the angles. See how to make a parallelogram video.
3. Fill in the blank: Parallelogram consecutive angles conjecture: The consecutive angles of a parallelogram are ___________________. (Remember that consecutive angles are next to each other.) Use the same parallelogram to figure this one out.
4. Fill in the blank: Parallelogram opposite sides conjecture: The opposite sides of a parallelogram are __________________. This time measure the length of the sides. Many of you should be able to figure this one out without even doing any work, the answer is obvious.
5. Fill in the blank: Parallelogram diagonals conjecture: The diagonals of a parallelogram __________________________________. Connect the opposite vertices with a diagonal and take measurements.
6. Fill in the blank: Double-edged straightedge conjecture: If two parallel lines are intersected by a second pair of parallel lines that are the same distance apart as the first pair, then the parallelogram formed is a _______________. See if you can create this on geogebra. The final answer is a not "square" however.
7. Fill in the blank: Rhombus diagonals conjecture: The diagonals of a rhombus are ___________________, and they ____________________________. Using a rhombus you've created on geogebra, connect the diagonals and measure angles and distances.
8. Fill in the blank: Rhombus angles conjecture: The _______________ of a rhombus ________________ the angles of the rhombus. Measure the angles.
9. Fill in the blank: Rectangle diagonals conjecture: The diagonals of a rectangle are _____________ and __________________. Make a rectangle, connect the opposite vertices, and measure angles and distances.
10. Fill in the blank: Square diagonals conjecture: The diagonals of a square are ______________, _______________ and ____________________. You should be able to figure this one out just by looking at all the work you've done to this point.
11. Homework: 1 through 6 on page 281, 1 through 11 on page 290.
Thursday, March 26, 2009
March 26th, 2009
1. Please read and do the investigation on page 273. Using geogebra, make a triangle. Then connect the midpoints of each side and figure out conjecture 42:
Three midsegments conjecture: The three midsegments of a triangle divide it into ______________________________________?
2. Now measure the lengths of each midsegment and each side. Figure out conjecture 43:
Triangle midsegment conjecture: A midsegment of a triangle is ______________
to the third side and ____________ half the length of the ________________.
3. Now do investigation #2 on page 274. Using geogebra, make a trapezoid. Then connect the midsegment of the non parallel sides. Measure the length of the three parallel sides. Fill in the last:
Trapezoid midsegment conjecture: The midsegment of a trapezoid is ______________
to the bases and is equal to the ____________________________________________.
Three midsegments conjecture: The three midsegments of a triangle divide it into ______________________________________?
2. Now measure the lengths of each midsegment and each side. Figure out conjecture 43:
Triangle midsegment conjecture: A midsegment of a triangle is ______________
to the third side and ____________ half the length of the ________________.
3. Now do investigation #2 on page 274. Using geogebra, make a trapezoid. Then connect the midsegment of the non parallel sides. Measure the length of the three parallel sides. Fill in the last:
Trapezoid midsegment conjecture: The midsegment of a trapezoid is ______________
to the bases and is equal to the ____________________________________________.
Wednesday, March 25, 2009
March 25th, 2009
1. For class today lets finish the investigations on page 267 and 268. Draw a new kite on geogabra and connect the diagonals. Finish conjecture c-36 and c-37. Now measure the angles and finish conjecture c-38.
2. Carefully read the bottom on page 267 to learn the vocabulary of trapezoids.
3. Draw a trapezoid on geogebra and measure the angles. Fill in conjecture c-39.
4. Now draw another trapezoid, only this time an isosceles trapezoid. Measure the angles and fill in conjecture c-40. Now connect the diagonals and measure them to fill in conjecture c-41.
5. Do problems 1-6 on page 269 and 270 for class work.
2. Carefully read the bottom on page 267 to learn the vocabulary of trapezoids.
3. Draw a trapezoid on geogebra and measure the angles. Fill in conjecture c-39.
4. Now draw another trapezoid, only this time an isosceles trapezoid. Measure the angles and fill in conjecture c-40. Now connect the diagonals and measure them to fill in conjecture c-41.
5. Do problems 1-6 on page 269 and 270 for class work.
Tuesday, March 24, 2009
March 24th, 2009
For class today:
1. Use geogabra for do the investigation on page 266.
2. Try to fill in the missing words in the conjectures.
3. Use geogabra to do the investigation on page 268.
4. Try to fill in the missing words in the conjectures.
5. Classwork, problems 1-6 on page 269 to 270.
Stay focused. These investigation are not easy! Work with a partner.
1. Use geogabra for do the investigation on page 266.
2. Try to fill in the missing words in the conjectures.
3. Use geogabra to do the investigation on page 268.
4. Try to fill in the missing words in the conjectures.
5. Classwork, problems 1-6 on page 269 to 270.
Stay focused. These investigation are not easy! Work with a partner.
Monday, March 23, 2009
Monday, March 23rd, 2009
Warm up: Review the following:The exterior angles sum conjecture: For any polygon, the sum of the measures of a set of exterior angles is 360 degrees.
This can easily be visualized by walking around a building that has any polygon shape. The angles that you will turn must sum up to 360, because you end up pointing in the direction you started.
The sum cannot be other than 360. Even if you have an 80 sided building. Every turn would just have a small angle measure. In fact, if you had a regular 80-gon, ("regular" meaning every side and angle is the same) then each angle would measure 360/80 which would be a very small 3.5 degrees each turn.
1. In class today, please do the Star Polygon exploration on page 264. Work together, stay focused. I will rotate around the room to help.
Friday, March 20, 2009
Good work in class today second period!
Sanya M. did a great job figuring out the Pentagon Sum Conjecture (The sum of the five angles of any pentagon is 540 degrees) and Ronald J. figured out the Polygon Sum Conjecture first (if it is a 15 sided figure, he said just subtract 2 and multiply by 180. So the formula is 180*(n-2). A shout out to Shifee A. and David W for solid investigations. Very happy with the overall focus of second period today!!!
For class Friday, March 20th, 2009
1. Please do the investigation on page 256. Use geogabra to create three polygon that look somewhat like the three in the book. Then measure the angles and share out.
At about 9:35 we should as a class answer the three conjectures on page 256 and 257:
Quadrilateral sum conjecture: The sum of the measure of the four angles of any quadrilateral is__________________.
Pentagon sum conjecture: The sum of the measure of the five angles of a pentagon is ________________.
Polygon sum conjecture: The sum of the measures of the n interior angles of an n-gon is
_______________________.
At about 9:50 please start the investigations on page 260 using geogebra again.
Click here for homework for this weekend
At about 9:35 we should as a class answer the three conjectures on page 256 and 257:
Quadrilateral sum conjecture: The sum of the measure of the four angles of any quadrilateral is__________________.
Pentagon sum conjecture: The sum of the measure of the five angles of a pentagon is ________________.
Polygon sum conjecture: The sum of the measures of the n interior angles of an n-gon is
_______________________.
At about 9:50 please start the investigations on page 260 using geogebra again.
Click here for homework for this weekend
Monday, March 16, 2009
For Class on Wednesday, March 18, 2009
Please work on the review to chapter 4, problem 1-37 on pages 249 to 252. We will be working on these problems all week, with an assessment on Friday. As the week goes by I want to post your answers and make videos for many of these problems. Work together, stay focused. Three half-days this week, but we can do a lot of work during half-days if we try!!! Work with each other, have fun!
1. Because of the SSS triangle, once the distances of the three sides are fixed the angles cannot change. Using triangles to build something makes everything very rigid. But if you use squares the angles can easily change, the square will become a rhombus
.
2. The triangle sum conjecture states that the sum of the measures of the angles in
every triangle is 180 degrees. It is the most important because it applies to all triangles, and many other conjectures rely upon it.
3. In an isosceles triangle the angle bisector of the vertex angle is also a median line and an altitude. Remember that a median line goes from the midpoint of one side of a triangle to the vertex opposite, an angle bisector splits an angle in half, and an altitude is perpendicular to the side opposite a vertex going through the vertex. See video here.
4. This is the question: What does the statement "the shortest distance between two points is the straight line between them" have to do with the Triangle Inequality conjecture? (Remember this conjecture states the sum of the length of any two sides of a triangle must be more than then third length.)
5. The four congruence shortcuts are SSS, SAS, ASA, and SAA. Can you explain why AAA is not a congruence shortcut?
6. Can you explain why SSA is not a congruence short cut? Hint: make two triangles on geogebra that have two sides the same and one angle (but not the included angle, which means the angle inbetween the two sides) but yet are different.
1. Because of the SSS triangle, once the distances of the three sides are fixed the angles cannot change. Using triangles to build something makes everything very rigid. But if you use squares the angles can easily change, the square will become a rhombus
.
2. The triangle sum conjecture states that the sum of the measures of the angles in
every triangle is 180 degrees. It is the most important because it applies to all triangles, and many other conjectures rely upon it.
3. In an isosceles triangle the angle bisector of the vertex angle is also a median line and an altitude. Remember that a median line goes from the midpoint of one side of a triangle to the vertex opposite, an angle bisector splits an angle in half, and an altitude is perpendicular to the side opposite a vertex going through the vertex. See video here.
4. This is the question: What does the statement "the shortest distance between two points is the straight line between them" have to do with the Triangle Inequality conjecture? (Remember this conjecture states the sum of the length of any two sides of a triangle must be more than then third length.)
5. The four congruence shortcuts are SSS, SAS, ASA, and SAA. Can you explain why AAA is not a congruence shortcut?
6. Can you explain why SSA is not a congruence short cut? Hint: make two triangles on geogebra that have two sides the same and one angle (but not the included angle, which means the angle inbetween the two sides) but yet are different.
Friday, March 13, 2009
For class on Friday, March 13, 2009
1. From 9:00am to 9:30am please work on problems 1 through 16 on pages 216 to 217. Some of you started this yesterday, some of you need to get started on it.
2. From 9:30 to 9:40 I need to the computers to be closed so that I can give you a lesson on the congruence shortcuts for triangles.
3. From 9:40 to 9:55 do investigation one on page 220. Use Geogabra or activestudio. I measure the three line segments for you, AC=3.6cm, BC=3.9cm and AB=5.1cm.
Complete the conjecture: SSS Congruence Conjecture: "If the three sides of one triangle are congruent to the three sides of another triangles, then ________________"
4. From 9:55 to the end of class some groups need to work on the investigation on page 221 (The SAS congruence shortcut) and some need to work on the investigation on page 225 (the ASA congruence shortcut). For those of you who do the first investigation complete the conjecture. For those of you who do the second, complete both the ASA conjecture and the SAA conjecture.
Homework will be posted here. If you want a hard copy of the homework please ask for it on the way out.
http://growometry1.wikispaces.com/
2. From 9:30 to 9:40 I need to the computers to be closed so that I can give you a lesson on the congruence shortcuts for triangles.
3. From 9:40 to 9:55 do investigation one on page 220. Use Geogabra or activestudio. I measure the three line segments for you, AC=3.6cm, BC=3.9cm and AB=5.1cm.
Complete the conjecture: SSS Congruence Conjecture: "If the three sides of one triangle are congruent to the three sides of another triangles, then ________________"
4. From 9:55 to the end of class some groups need to work on the investigation on page 221 (The SAS congruence shortcut) and some need to work on the investigation on page 225 (the ASA congruence shortcut). For those of you who do the first investigation complete the conjecture. For those of you who do the second, complete both the ASA conjecture and the SAA conjecture.
Homework will be posted here. If you want a hard copy of the homework please ask for it on the way out.
http://growometry1.wikispaces.com/
Thursday, March 12, 2009
Tuesday, March 10, 2009
For Class Wednesday, March 11th, 2009
1. Try
this problem for the warm up:
If you answered correctly, you ar
e ready for this question:
2. By now it should be 9:30am and we move on to the main lesson of today, which is 4.2 and 4.3.
Please ready page 204 in your textbook. The conjecture on page 205 reads as follows:
"Isosceles Triangle Conjecture:
If a triangle is isosceles, then its base angles are congruent."
Investigation 2 on page shows that the converse is also true (anyone remeber what the word "converse" means? It reverses an if-then statement. For example: If Shifee is in the classroom, then he is running around. The converse would be: If someone is running around the room then it is Shifee. Sometimes the converse is true, sometimes it isn't.)
"Converse of the isosceles Triangle conjecture: If a triangle has two congruent angles, then it is an isosceles triangle."
You should copy these two conjectures into your notebook.
Now the answer to problem 1 on page 206 is 79 degrees. Can you see why? It is because the three angles inside that triangle have to add up to 180, so 22 + the one base angle + the other base angle must equal 180. But the two base angles are congruent. So it amounts to solving for x using your 9th grade algebra: 22 + 2x = 180. So x=79. Now solve problems 2 through 6 on page 206 to 207.
3. The second lesson for today is 4.3, Triangle Inequalities.
Read page 213. Now can you make pictures on geogabra or activesudio that will support the following three conjectures:
Triangle inequality conjecture: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Side-Angle Inequality conjecture: In a triangle, if one side is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.
Triangle exterior angles conjecture: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
4. Homework will be problems 1 through 16 on page 216 and 217.
this problem for the warm up:If you answered correctly, you ar
e ready for this question:2. By now it should be 9:30am and we move on to the main lesson of today, which is 4.2 and 4.3.
Please ready page 204 in your textbook. The conjecture on page 205 reads as follows:
"Isosceles Triangle Conjecture:
If a triangle is isosceles, then its base angles are congruent."
Investigation 2 on page shows that the converse is also true (anyone remeber what the word "converse" means? It reverses an if-then statement. For example: If Shifee is in the classroom, then he is running around. The converse would be: If someone is running around the room then it is Shifee. Sometimes the converse is true, sometimes it isn't.)
"Converse of the isosceles Triangle conjecture: If a triangle has two congruent angles, then it is an isosceles triangle."
You should copy these two conjectures into your notebook.
Now the answer to problem 1 on page 206 is 79 degrees. Can you see why? It is because the three angles inside that triangle have to add up to 180, so 22 + the one base angle + the other base angle must equal 180. But the two base angles are congruent. So it amounts to solving for x using your 9th grade algebra: 22 + 2x = 180. So x=79. Now solve problems 2 through 6 on page 206 to 207.
3. The second lesson for today is 4.3, Triangle Inequalities.
Read page 213. Now can you make pictures on geogabra or activesudio that will support the following three conjectures:
Triangle inequality conjecture: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Side-Angle Inequality conjecture: In a triangle, if one side is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.
Triangle exterior angles conjecture: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
4. Homework will be problems 1 through 16 on page 216 and 217.
Sunday, March 8, 2009
Chapter 3 review
By the end of class today, I want everyone to have created 8 triangles, 4 acute, 4 obtuse or right, were the orthocenter is shown on one acute and one obtuse or right, circumcenter, incenter and centriod is shown on the others.
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