SAS and SSS

Mrs. Aitken’s Integrated 2
Unit 8 Similar and Congruent Triangles
8-5 Congruent Triangles: SAS and SSS
Warm-up
Write a two-column proof
Given: KJ ll GH; m

Mrs. Aitken’s Integrated 2
Unit 8 Similar and Congruent Triangles
SSS Postulate (side-side-side)
If three sides of one triangle are equal in measure to the corresponding
sides of another triangle, then the triangles are congruent.
Example 1
For each pair of triangles, tell whether there is enough info to prove that
the triangles are congruent.
a. b.
Solution 1
a. Yes, ▲SUV ≅▲ UST by SSS; ST = UV, TU = VS, SU = SU
b. Yes, ▲ABC ≅▲EDC
by SAS; AC = EC, BC = DC, and
m

Mrs. Aitken’s Integrated 2
Unit 8 Similar and Congruent Triangles
Example 3
Given AB = CD, AB ||CD
Prove ▲ABD
≅▲
ACD
Plan ahead - Show that m

Mrs. Aitken’s Integrated 2
Unit 8 Similar and Congruent Triangles
Example 5
uuuur uuuur
Which ray is an angle bisector, YW or XZ ?
Y
30°
50°
W
X
40°
40°
Z
uuuur
XZ
Example 6
In ▲ ABC , AB = AC, uuur AD bisects

Mrs. Aitken’s Integrated 2
Unit 8 Similar and Congruent Triangles
Example 8
Given: Parallelogram PQRS, diagonals PR and SQ bisect each other.
Prove: ▲SMP
≅▲
QMR
Solution 8
Statement
Justification
1. Parallelogram PQRS, diagonals 1. Given
PR and SQ bisect each other.
2. PM = MR; SM = MQ 2. Definition of segment bisector
3. m