What Does It Mean for Two Polygons to Be Congruent?

Review!

1. What does it mean for two polygons to be congruent?
2. What does it mean for two triangles to be congruent?
3. If two triangles are congruent, then how many pairs of corresponding congruent parts do they share?
4. Are there shortcuts?
5. SSS:

1. What does it mean?
2. Does it work?
3. Why? Include a picture

1. SSA:

1. What does it mean?
2. Does it work?
3. Why? Include a picture

1. SAS:

1. What does it mean?
2. Does it work?
3. Why? Include a picture

1. AAS:

1. What does it mean?
2. Does it work?
3. Why? Include a picture

1. ASA:

1. What does it mean?
2. Does it work?
3. Why? Include a picture

1. AAA:

1. What does it mean?
2. Does it work?
3. Why? Include a picture

1. The Crater Problem: Explain how NASA used congruent triangles to determine the diameter of a crater without actually measuring it. (Then read the book Hidden Figures, by Margot Lee Shetterley, which Mr. W-R ordered for the library, which tells the story of the African-American women who actually came up with these ideas. You can see the movie, too!)
2. Which shortcut explains why triangles are used in architecture? Explain!
3. Which shortcut ensures that scale models exist? Explain!
4. Like Thales before you, you are on the shore and see a boat in the distance. You mark off a 10 meter distance in the sand. From each end of the segment you made, you measure the angles to the ship, which are both 75 degrees. Now you make 75 degree angles on the other side (the beach side) of your segment in the sand until they meet at a vertex.

1. Draw a diagram of this situation using 1 cm=1inch.
2. How far away is the ship?
3. What congruence shortcut did you use?

1. What does CPCTC stand for? What does it mean? How can we use it?
2. Write a two column proof-structure to prove that: If a triangle is isosceles, then the triangle has two congruent angles.
3. Write a flow-chart proof structure to prove that: If a quadrilateral is a parallelogram, then the quadrilateral has two pairs of congruent opposite angles.
4. Explain why an equilateral triangle must be equiangular.
5. Must an equilateral quadrilateral also be equiangular? Explain!
6. When does SSA work?
7. Draw a circle. Place two points on the circle and connect them to the center by radii.

1. From both of the points you drew on the circle, now draw a line outside the circle until your two lines intersect outside the circle.
2. Draw the segment from this point of intersection in b. to the center of your circle.
3. What can you deduce about this figure?

1. Draw a triangle so that the angle bisector, “side bisector” (median), and perpendicular from an angle to the opposite side are all different lengths.
2. In what kind of triangle(s) are all these the same segment? Why?
3. What else did you learn?