![Page 1: 4.5 – Prove Triangles Congruent by ASA and AAS](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56813df8550346895da7d11b/html5/thumbnails/1.jpg)
4.5 – Prove Triangles Congruent by ASA and AAS
![Page 2: 4.5 – Prove Triangles Congruent by ASA and AAS](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56813df8550346895da7d11b/html5/thumbnails/2.jpg)
Angle-Side-Angle (ASA) Congruence Postulate
A B C D4cm 4cm
E F
CDAB
CA
DB
![Page 3: 4.5 – Prove Triangles Congruent by ASA and AAS](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56813df8550346895da7d11b/html5/thumbnails/3.jpg)
If two angles and the ______________ side of one triangle are _____________ to two angles and the ____________ side of a second triangle, then the two triangles are ________________.
included
includedcongruent
congruent
![Page 4: 4.5 – Prove Triangles Congruent by ASA and AAS](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56813df8550346895da7d11b/html5/thumbnails/4.jpg)
Angle-Angle-Side (AAS) Congruence Theorem
A B C D
E F
![Page 5: 4.5 – Prove Triangles Congruent by ASA and AAS](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56813df8550346895da7d11b/html5/thumbnails/5.jpg)
A B C D
E F
Angle-Angle-Side (AAS) Congruence Theorem
OR
![Page 6: 4.5 – Prove Triangles Congruent by ASA and AAS](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56813df8550346895da7d11b/html5/thumbnails/6.jpg)
If two angles and a _____________________ side of one triangle are _______________ to two angles and the corresponding ____________________ side of a second triangle, then the two triangles are ________________.
nonincluded
nonincluded
congruent
congruent
![Page 7: 4.5 – Prove Triangles Congruent by ASA and AAS](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56813df8550346895da7d11b/html5/thumbnails/7.jpg)
Does AAA work?
![Page 8: 4.5 – Prove Triangles Congruent by ASA and AAS](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56813df8550346895da7d11b/html5/thumbnails/8.jpg)
Does AAA work? NO!
![Page 9: 4.5 – Prove Triangles Congruent by ASA and AAS](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56813df8550346895da7d11b/html5/thumbnails/9.jpg)
Does ASS work?No!
There is no ASS in geometry!
![Page 10: 4.5 – Prove Triangles Congruent by ASA and AAS](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56813df8550346895da7d11b/html5/thumbnails/10.jpg)
Given:
Prove: ∆ABC ∆DCB
BDAC
CDAB
Statements Reasons
CDAB Given1. 1.
BDAC Given3. 3.BCD CBA alternate interior angles2. 2.
BCA CBD alternate interior angles4. 4.
BC BC Reflexive Prop.5. 5.
∆ABC ∆DCB ASA6. 6.
![Page 11: 4.5 – Prove Triangles Congruent by ASA and AAS](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56813df8550346895da7d11b/html5/thumbnails/11.jpg)
Given:
Prove: EA EBCABD
BDCAE at bisects
Statements Reasons
Given1. 1.
Given3. 3.
Def. of segment bisector2. 2.
ABD EBC vertical angles4. 4.
5. 5.∆ABD ∆EBC AAS
BCDB
BDCAE at bisects
EA
![Page 12: 4.5 – Prove Triangles Congruent by ASA and AAS](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56813df8550346895da7d11b/html5/thumbnails/12.jpg)
Decide whether the triangles are congruent. Explain your reasoning.
Yes, ASA
![Page 13: 4.5 – Prove Triangles Congruent by ASA and AAS](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56813df8550346895da7d11b/html5/thumbnails/13.jpg)
Decide whether the triangles are congruent. Explain your reasoning.
Yes, AAS
![Page 14: 4.5 – Prove Triangles Congruent by ASA and AAS](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56813df8550346895da7d11b/html5/thumbnails/14.jpg)
Decide whether the triangles are congruent. Explain your reasoning.
Yes, SAS
![Page 15: 4.5 – Prove Triangles Congruent by ASA and AAS](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56813df8550346895da7d11b/html5/thumbnails/15.jpg)
Decide whether the triangles are congruent. Explain your reasoning.
No, ASS doesn’t work!
![Page 16: 4.5 – Prove Triangles Congruent by ASA and AAS](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56813df8550346895da7d11b/html5/thumbnails/16.jpg)
Decide whether the triangles are congruent. Explain your reasoning.
Yes, AAS
![Page 17: 4.5 – Prove Triangles Congruent by ASA and AAS](https://reader035.vdocuments.mx/reader035/viewer/2022062422/56813df8550346895da7d11b/html5/thumbnails/17.jpg)
HW ProblemSectio
nPage # Assignment Spiral ?
s
4.5 WS 4.5 Worksheet 12-14