Proving Triangles are Congruent ASA and AAS

Proving Triangles are Proving Triangles are CongruentCongruent

ASA and AASASA and AAS

Proving Triangles are Proving Triangles are CongruentCongruent

ASA and AASASA and AASChapter 4.5Chapter 4.5

Objectives: To use the ASA and AAS Theorem to prove that triangles are Objectives: To use the ASA and AAS Theorem to prove that triangles are congruentcongruent

ASA Theorem•If two angles and the included side of one triangle, are congruent to the corresponding angles and side in a second triangle, then the triangles are congruent.

ABC XYZ — Why?

ASA Theorem

B

CA X

Z

Y

Use ASA in Proofs

Write a two-column proof.

Step Reason

Given

Def of Midpt.LEWL Given

L is the midpoint of WE

EDWR //W E Alternate Int. Thm.

RLW DLE Vertical Thm.

WRL EDL

ASA Thm.

Write a two-column proof.

Step Reason

Given

Reflexive PropertyBDBD

DABCCDAB //;//CBD ADB Alternate Int. Thm.CDB ABD Alternate Int. Thm.

ABD CDB

ASA Theorem.

AAS Theorem•If two angles and a non-included side of one triangle, are congruent to the corresponding angles and side in a second triangle, then the triangles are congruent.

ABC XYZ — Why?B

CA X

Z

Y

AAS Theorem

Write a two-column proof.

JNM KNL

IMPORTANT HINT:

When you are given overlapping triangles, draw them separately.

J

N

ML

N

K

Step Reason

Given

Reflexive PropertyJMKL

NKL NJM

GivenJNM KN LJNM KNL AAS Thm.

J

N

M L

N

K

HomeworkChapter 4-5• Pg 238

1-4, 8, 9, 15, 27

These are all These are all

two-column two-column proofs!!!proofs!!!

Video B7:40-

Interactive Lab: Proofs and Congruent Triangles