Download 4-3 Triangle Congruence by ASA and AAS

4-3 TRIANGLE CONGRUENCE BY ASA AND AAS (p. 194-201)
Do the following optional investigation by using a protractor.
Optional Investigation: Draw a segment that is 5 inches long. At the left endpoint, make
a 39  angle. At the right endpoint, make a 63 angle. Make sure that the rays of the two
angles intersect to create a triangle. Compare your triangle with the triangle of your
partner. Make a conjecture about how these triangles compare to each other.
Postulate 4-3 Angle-Side-Angle (ASA) Postulate
If two angles and the included side of one triangle are congruent to two angles
and the included side of another triangle, then the two triangles are congruent.
Example: Sketch two triangles and use tick marks to demonstrate the ASA Postulate.
Do 1 on p. 195.
Example: In the following diagram, it is given that B  E and T is the midpoint of
BE. Write a proof to prove that BAT  EOT.
B
O
T
A
E
There is a fourth method to prove two triangles congruent. You can use the ASA
Postulate to obtain this fourth method.
Example: Sketch two triangles that have two pairs of angles that are congruent and a
pair of nonincluded sides that are congruent. Use tick marks to indicate the congruent
parts. Why is the third pair of angles congruent? Place these new tick marks on the
triangles. What “old” method can you now use to prove these triangles congruent? By
doing this, you have just discovered a new way to prove triangles congruent.
Theorem 4-2 Angle-Angle-Side (AAS) Theorem
If two angles and a nonincluded side of one triangle are congruent to two angles
and the corresponding nonincluded side of another triangle, then the triangles are
congruent.
Example: Sketch two triangles and use tick marks to demonstrate the AAS Theorem.
Example:
W
Z
X
Y
Given: X  Z, WX
ZY
Prove: XWY  ZYW
Prove this conclusion by writing a paragraph, flow, or two-column proof.
Do 4 on p. 196.
Homework p. 197-201: 3,6,7,9,11,13,14,18,19,25,28,33,42,43,46,49,51
51. 24  36  24  36