Lesson 5.2 Proving Triangles are Congruent: SSS and SAS

Pages 241 - 244

Side-Side-Side Congruence Postulate (SSS)

If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

Side – BO ≅ MASide – OW ≅ ANSide – BW ≅ MNTherefore, by SSS, BOW ≅ MAN

Does the diagram give enough information to show that the triangles are congruent?

M P

O

N

Side-Angle-Side Congruence Postulate (SAS)

If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.

Side – BO ≅ MAAngle - O ≅ ASide – OW ≅ ANTherefore, by SAS, BOW ≅ MAN

Does the diagram give enough information to use the SAS Congruence Postulate?

T S R

L

P

R

A

H

Writing Proofs

A proof is a convincing argument that shows why a statement is true. A two-column proof has numbered statements and reasons that show the logical order of the argument. Each statement has a reason listed to its right.

How to Write a Proof

• List the given information first• Use the information from the diagram• Give a reason for every statement• Use given information, definitions, postulates,

and theorems as the “Reasons”• List statements in order.• End the proof with the statement that you are

trying to prove.

Write a 2-Column Proof that shows JKL ≅ NML

Given: JL ≅ NL and L is the midpoint of KMProve: JKL ≅ NMLStatements: Reasons:1. 1.2. 2.3. 3.4. 4.5. 5.

J

KN

ML

Write a 2-Column Proof that shows DRA ≅ DRG

Given: DR ≅ AG and RA ≅ RGProve: DRA ≅ DRGStatements: Reasons:1. 1.2. 2.3. 3.4. 4.5. 5.6. 6.

A G

D

R

Fill in the missing statements and missing reasons.

Given: CB ≅ CE, AC ≅ DCProve: BCA ≅ ECDStatements: Reasons:1.CB ≅ CE 1.2. 2. Given3. BCA ≅ ECD 3.4. BCA ≅ ECD 4.

B DC

A E

Assignment:

Pages 245 – 248#16 – 26 even, #34, #36, #40

And5.2 Practice B Worksheet