LESSON 4-2

TRIANGLE CONGRUENCE

BY SSS AND SAS

Objective: Prove two triangles are congruent

using the SSS and SAS Postulates.

Key Concepts

SSS (Side-Side-Side) Postulate

If the three sides of one triangle are congruent to the three

sides of another triangle, then the two triangles are

congruent.

(NOTES…DNG page 75-76)

XY AY

MY

Reflexive Property of Congruence

SSS Postulate

(DNG page 75) Proving Triangles Congruent

Key Concepts

SAS (Side-Angle-Side) Postulate

If two sides and an included angle of one triangle are congruent

to two sides and an included angle of another triangle, then the

two triangles are congruent.

Vocabulary…

What other information do you need to prove ADC BCD by SAS?

Reflexive Property of Congruence

ADC BCD

SAS

From the information given, can you prove RSG RSH? Explain.

(DNG page 76)

Reflexive Property of Congruence

SAS

X

X

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Practice 4-2 Triangle Congruence by SSS & SAS

Decide whether you can use the SSS or SAS Postulate to prove the triangles congruent. If so, write

the congruence statement, and identify the postulate. If not, write not possible.

X

ADB ≅ CDB by SAS

not possible not possible

TUS ≅ XWV by SSS not possible DEC ≅ GHF by SAS

Practice 4-2 Triangle Congruence by SSS & SAS

Decide whether you can use the SSS or SAS Postulate to prove the triangles congruent. If so, write

the congruence statement, and identify the postulate. If not, write not possible.

MKL ≅ KMJ by SAS PRN ≅ PRQ by SSS

X

not possible

Draw a triangle. Label the vertices A, B, and C. B

A C

BCA

BCAB and

B and A

AC

Practice 4-2 Triangle Congruence by SSS & SAS

14. Developing Proof Supply the reasons in this proof.

Statements Reasons

1. 1.

2. 2.

3. 3.

Given

CAAC Reflexive Property of ≅

ABC ≅ CDA SAS Postulate

X

Practice 4-2 Triangle Congruence by SSS & SAS

15. Write a proof.

Statements Reasons

1. 1.

2. 2.

3. 3.

Given

DFE ≅ HFG Vertical s are ≅.

DFE ≅ HFG SAS Postulate

Do not forget to take your HOMEWORK assignment sheet!!!