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.
Monday, April 13, 2009
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.
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