Triangle Congruence: by SSS and SASGeometry H2 (Holt 4-5) K. Santos

Side-Side-Side (SSS) Congruence Postulate (4-5-1)If the three sides of one triangle are congruent to the three sides of another triangle , then the two triangles are congruent. A DGiven: E

B C F

Then:

Included Angle

Included angle—is an angle formed by two adjacent sides. A

B C

< B is the included angle between sides and

Side-Angle-Side (SAS) Congruence Postulate (4-5-2)If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Given: A J K

< A K B C L

Then:

Please note both angles must be included between the sides!!!

Example—Writing a congruence statementWrite a congruence statement for the congruent triangles and name the postulate you used to know the triangles were congruent.

1. D R S 2. A

F E T B C D

Example—what other information is needed What other information do you need to prove the two triangles congruent by SSS or SAS?

1. M T 2. G H Q

U R N O V I S

Example—explain triangle congruence

Use the SSS or SAS postulate to explain why the triangles are congruent.

A B

D C

Example—verifying triangle congruenceShow that the triangles are congruent for the given value of the variable. , a = 3

U X

4 2 a 3a - 5 W

V 3 Z a – 1 Y

Proof

QGiven: bisects <RQS

Prove: R P S

Statements Reasons

Proof

Given: E G Prove:

F HStatements Reasons