4.5 – prove triangles congruent by asa and aas
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4.5 – Prove Triangles Congruent by ASA and AAS. Angle-Side-Angle (ASA) Congruence Postulate. E. F. 4 cm. B. C. 4 cm. D. A. - PowerPoint PPT PresentationTRANSCRIPT
4.5 – Prove Triangles Congruent by ASA and AAS
Angle-Side-Angle (ASA) Congruence Postulate
A B C D4cm 4cm
E F
CDAB
CA
DB
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
Angle-Angle-Side (AAS) Congruence Theorem
A B C D
E F
A B C D
E F
Angle-Angle-Side (AAS) Congruence Theorem
OR
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
Does AAA work?
Does AAA work? NO!
Does ASS work?No!
There is no ASS in geometry!
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.
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
Decide whether the triangles are congruent. Explain your reasoning.
Yes, ASA
Decide whether the triangles are congruent. Explain your reasoning.
Yes, AAS
Decide whether the triangles are congruent. Explain your reasoning.
Yes, SAS
Decide whether the triangles are congruent. Explain your reasoning.
No, ASS doesn’t work!
Decide whether the triangles are congruent. Explain your reasoning.
Yes, AAS
HW ProblemSectio
nPage # Assignment Spiral ?
s
4.5 WS 4.5 Worksheet 12-14