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4-5 Proving Triangles Congruent – ASA, AAS You proved triangles congruent using SSS and SAS. Use the ASA Postulate to test for congruence.

4-5 Proving Triangles Congruent – ASA, AAS You proved triangles congruent using SSS and SAS. Use the ASA Postulate to test for congruence

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Page 1: 4-5 Proving Triangles Congruent – ASA, AAS You proved triangles congruent using SSS and SAS. Use the ASA Postulate to test for congruence

4-5 Proving Triangles Congruent – ASA, AAS

You proved triangles congruent using SSS and SAS.

• Use the ASA Postulate to test for congruence.

Page 2: 4-5 Proving Triangles Congruent – ASA, AAS You proved triangles congruent using SSS and SAS. Use the ASA Postulate to test for congruence

Angle-Side-Angle Congruence Postulate (ASA)

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Page 3: 4-5 Proving Triangles Congruent – ASA, AAS You proved triangles congruent using SSS and SAS. Use the ASA Postulate to test for congruence

Page 275

Page 4: 4-5 Proving Triangles Congruent – ASA, AAS You proved triangles congruent using SSS and SAS. Use the ASA Postulate to test for congruence

Use ASA to Prove Triangles Congruent

4. Alternate Interior Angles4. W E

Statements Reasons

1. Given1. L is the midpoint of WE.____

3. Given3.

2. Midpoint Theorem2.

5. Vertical Angles Theorem5. WLR ELD

6. ASA6. ΔWRL ΔEDL

Page 5: 4-5 Proving Triangles Congruent – ASA, AAS You proved triangles congruent using SSS and SAS. Use the ASA Postulate to test for congruence

A. SSS B. SAS

C. ASA D. AAS

Fill in the blank in the following paragraph proof.

Page 6: 4-5 Proving Triangles Congruent – ASA, AAS You proved triangles congruent using SSS and SAS. Use the ASA Postulate to test for congruence

Side-Angle-Side Congruence Postulate (SAA)

If two angles and a side opposite one of them in one triangle are congruent to the corresponding parts of another triangle, then the two triangles are congruent.

Page 7: 4-5 Proving Triangles Congruent – ASA, AAS You proved triangles congruent using SSS and SAS. Use the ASA Postulate to test for congruence
Page 8: 4-5 Proving Triangles Congruent – ASA, AAS You proved triangles congruent using SSS and SAS. Use the ASA Postulate to test for congruence

Try It

If possible, what is the congruence statement for this pair of triangles? If the triangles are not congruent, say so.

A

B

C

M

NO

Needs more information

Page 9: 4-5 Proving Triangles Congruent – ASA, AAS You proved triangles congruent using SSS and SAS. Use the ASA Postulate to test for congruence

Try It

If possible, what is the congruence statement for this pair of triangles? If the triangles are not congruent, say so.

SAA;RQPDEF

R

D

E F

20°

130°

P Q

20°

130°

Page 10: 4-5 Proving Triangles Congruent – ASA, AAS You proved triangles congruent using SSS and SAS. Use the ASA Postulate to test for congruence

Write a paragraph proof.

Proof: NKL NJM, KL MN, and N N by the Reflexive property. Therefore, ΔJNM ΔKNL by AAS. By CPCTC, LN MN.

__ ___

_____

Page 11: 4-5 Proving Triangles Congruent – ASA, AAS You proved triangles congruent using SSS and SAS. Use the ASA Postulate to test for congruence

A. SSS B. SAS

C. ASA D. AAS

Complete the following flow proof.

Page 12: 4-5 Proving Triangles Congruent – ASA, AAS You proved triangles congruent using SSS and SAS. Use the ASA Postulate to test for congruence

A. SSS

B. SAS

C. ASA

D. AAS

The curtain decorating the window forms 2 triangles at the top. B is the midpoint of AC. AE = 13 inches and CD = 13 inches. BE and BD each use the same amount of material, 17 inches. Which method would you use to prove ΔABE ΔCBD?

Page 13: 4-5 Proving Triangles Congruent – ASA, AAS You proved triangles congruent using SSS and SAS. Use the ASA Postulate to test for congruence

Page 278

Page 14: 4-5 Proving Triangles Congruent – ASA, AAS You proved triangles congruent using SSS and SAS. Use the ASA Postulate to test for congruence

What are the four short cuts to prove triangles congruent?

• Side-Side-Side (SSS)• Side-Angle-Side (SAS)• Angle-Side-Angle (ASA)• Side-Angle-Angle (SAA)

Page 15: 4-5 Proving Triangles Congruent – ASA, AAS You proved triangles congruent using SSS and SAS. Use the ASA Postulate to test for congruence

4-5 Assignment

Page 278, 1, 4, 9, 10• Write as a two column proof.• Write out Given and Prove.• Draw the figure.