Download Geometry Ch. 4.5: Proving Triangles Congruent: ASA, and AAS In

Name: _____________________________
Geometry Ch. 4.5: Proving Triangles Congruent: ASA, and AAS
In the last section, we learned that we could use Side-Side-Side and Side-Angle-Side to show that two triangles
are congruent. We will now learn the last 2 which are Angle-Side-Angle and Angle-Angle-Side.
Postulate 4.3: Angle-Side-Angle (ASA)
Congruence
If two angles and the _____________side of one
triangle are congruent to two angles and the included
side of another triangle, then the triangles are
______________.
Theorem 4.5: Angle-Angle-Side (AAS)
Congruence
If two angles and the __________________ side of
one triangle are congruent to the corresponding two
angles and side of a second triangle, then the two
triangles are ________________.
Concept Summary
SSS
SAS
Proof of Theorem 4.5
Given: ∠L ≅ ∠Q , ∠M ≅ ∠R , MN ≅ RS
Prove: △LMN ≅△QRS
ASA
AAS
Name: _____________________________
Write a two-column proof
Given: L is the midpoint of WE
WR ! ED
Prove: △WRL ≅△EDL
Write a paragraph proof
Given: ∠NKL ≅ ∠NJM
KL ≅ JM
Prove: LN ≅ MN
Geometry Ch. 4.5: Proving Triangles Congruent: ASA, and AAS