Five-Minute Check (over Lesson 4–3)

Then/Now

New Vocabulary

Postulate 4.1: Side-Side-Side (SSS) Congruence

Example 1: Use SSS to Prove Triangles Congruent

Example 2: Standard Test Example

Postulate 4.2: Side-Angle-Side (SAS) Congruence

Example 3: Real-World Example: Use SAS to Prove Triangles are Congruent

Example 4: Use SAS or SSS in Proofs

Over Lesson 4–3

A. A

B. B

C. C

D. D A B C D

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A. ΔLMN ΔRTS

B. ΔLMN ΔSTR

C. ΔLMN ΔRST

D. ΔLMN ΔTRS

Write a congruence statement for the triangles.

Over Lesson 4–3

A. A

B. B

C. C

D. D A B C D

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A. L R, N T, M S

B. L R, M S, N T

C. L T, M R, N S

D. L R, N S, M T

Name the corresponding congruent angles for the congruent triangles.

Over Lesson 4–3

A. A

B. B

C. C

D. D A B C D

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Name the corresponding congruent sides for the congruent triangles.

A. LM RT, LN RS, NM ST

B. LM RT, LN LR, LM LS

C. LM ST, LN RT, NM RS

D. LM LN, RT RS, MN ST

______ ___ ______ ___

___ ___ ___ ___ ___ ___

___ ______ ___ ___ ___

___ ___ ___ ___ ___ ___

Over Lesson 4–3

A. A

B. B

C. C

D. D A B C D

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A. 1

B. 2

C. 3

D. 4

Refer to the figure. Find x.

Over Lesson 4–3

A. A

B. B

C. C

D. D A B C D

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A. 30

B. 39

C. 59

D. 63

Refer to the figure.Find m A.

Over Lesson 4–3

A. A

B. B

C. C

D. D A B C D

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Given that ΔABC ΔDEF, which of the following statements is true?

A. A E

B. C D

C. AB DE

D. BC FD___ ___

___ ___

You proved triangles congruent using the definition of congruence. (Lesson 4–3)

• Use the SSS Postulate to test for triangle congruence.

• Use the SAS Postulate to test for triangle congruence.

• included angle

Use SSS to Prove Triangles Congruent

Write a 2-column proof.

Prove: ΔQUD ΔADUGiven: QU AD, QD AU

___ ___ ___ ___

A. A

B. B

C. C

D. D A B C D

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Write a two-column proof.Given: AC AB

D is the midpoint of BC.Prove: ΔADC ΔADB

___ ___

EXTENDED RESPONSE Triangle DVW has vertices D(–5, –1), V(–1, –2), and W(–7, –4). Triangle LPM has vertices L(1, –5), P(2, –1), and M(4, –7).a. Graph both triangles on the same coordinate

plane.b. Use your graph to make a conjecture as to

whether the triangles are congruent. Explain your

reasoning.c. Write a logical argument that uses coordinate

geometry to support the conjecture you made in

part b.

Solve the Test Item

a.

b. From the graph, it appears that the triangles have the same shapes, so we conjecture that they are congruent.

c. Use the Distance Formula to show all corresponding sides have the same measure.

Answer: WD = ML, DV = LP, and VW = PM. By definition of congruent segments, all corresponding segments are congruent. Therefore, ΔWDV ΔMLP by SSS.

Use SAS to Prove Triangles are Congruent

ENTOMOLOGY The wings of one type of moth form two triangles. Write a two-column proof to prove that ΔFEG ΔHIG if EI HF, and G is the midpoint of both EI and HF.

Use SAS to Prove Triangles are Congruent

3. 3. FGE HGI

2. 2.

Prove: ΔFEG ΔHIG

4. 4. ΔFEG ΔHIG

Given: EI HF; G is the midpoint of both EI and HF.

1. 1. EI HF; G is the midpoint ofEI; G is the midpoint of HF.

Proof:ReasonsStatements

A. A

B. B

C. C

D. D A B C D

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3. 3. ΔABG ΔCGB

2. 2.

1.

ReasonsProof:Statements

1.

Use SAS or SSS in Proofs

Write a 2-column proof.

Prove: Q S

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

Write a 2-column proof.