proving triangles are congruent asa and aas
DESCRIPTION
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 PresentationTRANSCRIPT
![Page 1: Proving Triangles are Congruent ASA and AAS](https://reader036.vdocuments.us/reader036/viewer/2022081506/56813a2c550346895da213d5/html5/thumbnails/1.jpg)
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
![Page 2: Proving Triangles are Congruent ASA and AAS](https://reader036.vdocuments.us/reader036/viewer/2022081506/56813a2c550346895da213d5/html5/thumbnails/2.jpg)
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.
![Page 3: Proving Triangles are Congruent ASA and AAS](https://reader036.vdocuments.us/reader036/viewer/2022081506/56813a2c550346895da213d5/html5/thumbnails/3.jpg)
ABC XYZ — Why?
ASA Theorem
B
CA X
Z
Y
![Page 4: Proving Triangles are Congruent ASA and AAS](https://reader036.vdocuments.us/reader036/viewer/2022081506/56813a2c550346895da213d5/html5/thumbnails/4.jpg)
Use ASA in Proofs
Write a two-column proof.
![Page 5: Proving Triangles are Congruent ASA and AAS](https://reader036.vdocuments.us/reader036/viewer/2022081506/56813a2c550346895da213d5/html5/thumbnails/5.jpg)
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.
![Page 6: Proving Triangles are Congruent ASA and AAS](https://reader036.vdocuments.us/reader036/viewer/2022081506/56813a2c550346895da213d5/html5/thumbnails/6.jpg)
Write a two-column proof.
![Page 7: Proving Triangles are Congruent ASA and AAS](https://reader036.vdocuments.us/reader036/viewer/2022081506/56813a2c550346895da213d5/html5/thumbnails/7.jpg)
Step Reason
Given
Reflexive PropertyBDBD
DABCCDAB //;//CBD ADB Alternate Int. Thm.CDB ABD Alternate Int. Thm.
ABD CDB
ASA Theorem.
![Page 8: Proving Triangles are Congruent ASA and AAS](https://reader036.vdocuments.us/reader036/viewer/2022081506/56813a2c550346895da213d5/html5/thumbnails/8.jpg)
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.
![Page 9: Proving Triangles are Congruent ASA and AAS](https://reader036.vdocuments.us/reader036/viewer/2022081506/56813a2c550346895da213d5/html5/thumbnails/9.jpg)
ABC XYZ — Why?B
CA X
Z
Y
AAS Theorem
![Page 10: Proving Triangles are Congruent ASA and AAS](https://reader036.vdocuments.us/reader036/viewer/2022081506/56813a2c550346895da213d5/html5/thumbnails/10.jpg)
Write a two-column proof.
JNM KNL
![Page 11: Proving Triangles are Congruent ASA and AAS](https://reader036.vdocuments.us/reader036/viewer/2022081506/56813a2c550346895da213d5/html5/thumbnails/11.jpg)
IMPORTANT HINT:
When you are given overlapping triangles, draw them separately.
J
N
ML
N
K
![Page 12: Proving Triangles are Congruent ASA and AAS](https://reader036.vdocuments.us/reader036/viewer/2022081506/56813a2c550346895da213d5/html5/thumbnails/12.jpg)
Step Reason
Given
Reflexive PropertyJMKL
NKL NJM
GivenJNM KN LJNM KNL AAS Thm.
J
N
M L
N
K
![Page 13: Proving Triangles are Congruent ASA and AAS](https://reader036.vdocuments.us/reader036/viewer/2022081506/56813a2c550346895da213d5/html5/thumbnails/13.jpg)
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