Download CCII Congruence Day 3 Name #______ Triangle Congruence

CCII
Congruence Day 3
Name _________________________________________#______
Triangle Congruence Shortcuts Investigation (Part 3 and 4)
Part 3
For this activity, you will need:
* a sheet of patty paper
* a pencil
* a ruler
(1) We are going to create a triangle using the three angles given below. First, draw a segment of any
length near the bottom edge of your patty paper. Label the segment PR.
(2) Trace P on the left end of the segment and trace R on the right end of the segment.
(3) Extend the side lengths until they intersect. Label the intersection point Q.
(4) Check to be sure the measure of Q matches with the angle given below.
(5)
(a)
(b)
(c)
Compare your triangle with a group member’s triangle.
Are all three pairs of corresponding angles the same measure? _____________
Are all three pairs of corresponding sides the same length? ______________
Are the triangles congruent? __________
(6) What can we conclude about triangle congruence when all angles (AAA) are congruent?
Part 4
For this activity, you will need:
* a sheet of patty paper
* a pencil
* a ruler
(1) We are going to create a triangle using the two angles and side given on the next page. First, very
carefully trace and label MT on near the bottom edge of a sheet of patty paper.
(2) Trace M on the left end of the segment and T on the right end of the segment. (Note: You will have
to rotate the paper to trace the angles properly.)
(3) Extend the sides of the triangle until they intersect. Label the point of intersection A.
(4)
(a)
(b)
(c)
Compare your triangle with a group member’s triangle.
Are all three pairs of corresponding angles the same measure? _____________
Are all three pairs of corresponding sides the same length? ______________
Are the triangles congruent? __________
(5) What can we conclude about triangle congruence when two angles and the included side (ASA) are
congruent?
Comparing Parts 3 and 4:
In both Part 3 and Part 4 activities, we started with a line segment and traced angles on the endpoints.
We then extended the sides to find the third angle. In Part 3, this method did not create two congruent
triangles. In Part 4, this method did create two congruent triangles. Using complete sentences, explain
why there was a difference in the congruence of triangles in the two different activities.