HOMEWORK: WS - Congruent Triangles Proving Δ’s are using: SSS, SAS, HL, ASA, & AAS.
Proving Triangles are Congruent ASA and AAS
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Proving Triangles are Proving Triangles are Congruent Congruent ASA and AAS ASA and AAS Chapter 4.5 Chapter 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 congruent congruent
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Proving Triangles are Congruent ASA and AAS. Chapter 4.5 Objectives: To use the ASA and AAS Theorem to prove that triangles are congruent. ASA Theorem. - PowerPoint PPT Presentation
Transcript of 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
