Five-Minute Check (over Lesson 4–3)Then/NowNew VocabularyPostulate 4.1: Side-Side-Side (SSS) CongruenceExample 1: Use SSS to Prove Triangles CongruentExample 2: Standard Test ExamplePostulate 4.2: Side-Angle-Side (SAS) CongruenceExample 3: Real-World Example: Use SAS to Prove

Triangles are CongruentExample 4: Use SAS or SSS in Proofs

Over Lesson 4–3

A. AB. BC. CD. 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. AB. BC. CD. 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. AB. BC. CD. 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. AB. BC. CD. 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. AB. BC. CD. 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. AB. BC. CD. 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 flow proof.

Prove: ΔQUD ΔADU

Given: QU AD, QD AU ___ ___ ___ ___

Use SSS to Prove Triangles Congruent

Answer: Flow Proof:

A. AB. BC. CD. D

A B C D

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Which information is missing from the flowproof?Given: AC AB

D is the midpoint of BC.Prove: ΔADC ΔADB

___ ___

A. AC AC

B. AB AB

C. AD AD

D. CB BC

___ ___

___ ___

___ ___

___ ___

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.

Read the Test ItemYou are asked to do three things in this problem. In part a, you are to graph ΔDVW and ΔLPM on the same coordinate plane. In part b, you should make a conjecture that ΔDVW ΔLPM or ΔDVW ΔLPM based on your graph. Finally, in part c, you are asked to prove your conjecture.

/

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.

1. A2. B3. C

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A. yes

B. no

C. cannot be determined

Determine whether ΔABC ΔDEF for A(–5, 5), B(0, 3), C(–4, 1), D(6, –3), E(1, –1), and F(5, 1).

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. Vertical Angles Theorem

3. FGE HGI

2. Midpoint Theorem2.

Prove: ΔFEG ΔHIG

4. SAS4. ΔFEG ΔHIG

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

1. Given1. EI HF; G is the midpoint ofEI; G is the midpoint of HF.

Proof:ReasonsStatements

A. AB. BC. CD. D

A B C D

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A. Reflexive B. Symmetric

C. Transitive D. Substitution

3. SSS3. ΔABG ΔCGB

2. _________2. ? Property

1. Reasons

Proof:Statements

1. Given

Use SAS or SSS in Proofs

Write a paragraph proof.

Prove: Q S

Use SAS or SSS in Proofs

Answer:

A. AB. BC. CD. D

A B C D

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Choose the correct reason to complete the following flow proof.

A. Segment Addition PostulateB. Symmetric PropertyC. Midpoint TheoremD. Substitution