Page 91 - Math Course 3 (Book 2)

ASA and AAS Postulates

Determine if Triangles Are Congruent
Let’s Begin
Example

Triangle Congruence Proof
STANCES
When Mr. Gomez puts his hands on his hips, he
Example forms two triangles with his upper body and arms.
Suppose his arm lengths AB and DE measure 9
inches, and AC and EF measure 11 inches.
Write a paragraph proof.
R E
L Also suppose that you are given that BC ≅ DF.
Determine whether △ABC ≅ △EDF.
Justify your answer.
W
D

Given: L is the midpoint of WE ; WR || ED
Prove: △WRL ≅ △EDL

Proof: ∠W ≅ ∠E because alternate interior are
congruent when line are parallel. By the
Midpoint Theorem, WL ≅ EL. Since B D
vertical angles are congruent,
∠WLR ≅ ∠ELD. △WRL ≅ △EDL by ASA. A E

Use AAS in Proofs C F

Example Explore
We are given measurements of two sides of each
triangle. We need to determine whether the two
triangles are congruent.
Write a flow proof. J K
Plan
Since AB = DE = 9, AB ≅ DE. Likewise,
L M
AC = EF = 11, AC ≅ EF. We are given BC ≅ DF.
Given: ∠NKL ≅ ∠NJM Check each possibility using the five methods you

KL ≅ JM N know.
Prove: LN ≅ MN

Proof: Solve
We are given information about three sides. Since
∠NKL ≅ ∠NJM KL ≅ JM ∠N ≅ ∠N all three pairs of corresponding sides of the
Given Given Reflexive Property triangles are congruent, ΔABC ≅ ΔEDF by SSS.

Examine
△JNM ≅ △KNL You can measure each angle in ΔABC and ΔEDF to

AAS verify that ∠A ≅ ∠E, ∠B ≅ ∠D, and ∠C ≅ ∠F

LN ≅ MN Answer ΔABC ≅ ΔEDF by SSS.
CPCTC

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