Five-Minute Check (over Lesson 4–4)

NGSSS

Then/Now

New Vocabulary

Postulate 4.3: Angle-Side-Angle (ASA) Congruence

Example 1:Use ASA to Prove Triangles Congruent

Theorem 4.5:Angle-Angle-Side (AAS) Congruence

Example 2:Use AAS to Prove Triangles Congruent

Example 3:Real-World Example: Apply Triangle Congruence

Concept Summary: Proving Triangles Congruent

Over Lesson 4–4

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. SSS

B. ASA

C. SAS

D. not possible

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.

Over Lesson 4–4

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. SSS

B. ASA

C. SAS

D. not possible

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.

Over Lesson 4–4

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. SAS

B. AAS

C. SSS

D. not possible

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.

Over Lesson 4–4

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. SSA

B. ASA

C. SSS

D. not possible

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.

Over Lesson 4–4

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. AAA

B. SAS

C. SSS

D. not possible

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.

Over Lesson 4–4

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

Given A R, what sides must you know to be congruent to prove ΔABC ΔRST by SAS?

A.

B.

C.

D.

MA.912.G.4.6 Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles.

MA.912.G.4.8 Use coordinate geometry to prove properties of congruent, regular, and similar triangles.

You proved triangles congruent using SSS and SAS. (Lesson 4–4)

• Use the ASA Postulate to test for congruence.

• Use the AAS Theorem to test for congruence.

• included side

Use ASA to Prove Triangles Congruent

Write a two column proof.

Use ASA to Prove Triangles Congruent

4. Alternate Interior Angles4. W E

Proof: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

A. A

B. B

C. C

D. D

A B C D

0% 0%0%0%

A. SSS B. SAS

C. ASA D. AAS

Fill in the blank in the following paragraph proof.

Use AAS to Prove Triangles Congruent

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.

__ ___

__ ___

A. A

B. B

C. C

D. D

A B C D

0% 0%0%0%

A. SSS B. SAS

C. ASA D. AAS

Complete the following flow proof.

Apply Triangle Congruence

MANUFACTURING Barbara designs a paper template for a certain envelope. She designs the top and bottom flaps to be isosceles triangles that have congruent bases and base angles. If EV = 8 cm and the height of the isosceles triangle is 3 cm,find PO.

Apply Triangle Congruence

• ΔENV ΔPOL by ASA.

In order to determine the length of PO, we must first prove that the two triangles are congruent.

____

• NV EN by definition of isosceles triangle____ ____

• EN PO by CPCTC.____ ____

• NV PO by the Transitive Property of Congruence.____ ____

Since the height is 3 centimeters, we can use the Pythagorean theorem to calculate PO. The altitude of the triangle connects to the midpoint of the base, so each half is 4. Therefore, the measure of PO is 5 centimeters.

____

___

Answer: PO = 5 cm

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

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?