4.5 – prove triangles congruent by asa and aas

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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 Presentation

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Page 1: 4.5 – Prove Triangles Congruent by ASA and AAS

4.5 – Prove Triangles Congruent by ASA and AAS

Page 2: 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

Page 3: 4.5 – Prove Triangles Congruent by ASA and AAS

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

Angle-Angle-Side (AAS) Congruence Theorem

A B C D

E F

Page 5: 4.5 – Prove Triangles Congruent by ASA and AAS

A B C D

E F

Angle-Angle-Side (AAS) Congruence Theorem

OR

Page 6: 4.5 – Prove Triangles Congruent by ASA and AAS

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

Does AAA work?

Page 8: 4.5 – Prove Triangles Congruent by ASA and AAS

Does AAA work? NO!

Page 9: 4.5 – Prove Triangles Congruent by ASA and AAS

Does ASS work?No!

There is no ASS in geometry!

Page 10: 4.5 – Prove Triangles Congruent by ASA and AAS

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

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

Decide whether the triangles are congruent. Explain your reasoning.

Yes, ASA

Page 13: 4.5 – Prove Triangles Congruent by ASA and AAS

Decide whether the triangles are congruent. Explain your reasoning.

Yes, AAS

Page 14: 4.5 – Prove Triangles Congruent by ASA and AAS

Decide whether the triangles are congruent. Explain your reasoning.

Yes, SAS

Page 15: 4.5 – Prove Triangles Congruent by ASA and AAS

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

Decide whether the triangles are congruent. Explain your reasoning.

Yes, AAS

Page 17: 4.5 – Prove Triangles Congruent by ASA and AAS

HW ProblemSectio

nPage # Assignment Spiral ?

s

4.5 WS 4.5 Worksheet 12-14

4.4 Proving Triangles are Congruent: ASA and AAS Geometry

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