Topic: U7L5 Proving Congruence--SSS, SAS
EQ: What is meant by SSS and SAS and how do I use them in
proofs?
Congruent Triangles
• Means that corresponding parts are congruent,
• Matching sides and angles will be congruent
A
B
C
Z
Y
X
Naming
• ORDER MATTERS!!!!
Example 1
• If two triangles are congruent…– Name all congruent angles
– Name all congruent sides
S
R
T
Y
X
Z
Reminder…
• If two angles of one triangle are congruent to two angles of another triangle then the 3rd angles are congruent
Keep in mind
• You can flip, turn or slide congruent triangles and they will maintain congruency!!
Side-Side-Side Congruence (SSS)
• If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent
A
B
C
X Y
Z
XYZABC
Included angles
Side-Angle-Side Congruence (SAS)
• If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.
A
B
C
DE
F
FDEABC
Given: Triangle CDE is an isosceles triangle. G is the midpoint of CE.
Prove:
CG
E
D
EDGCDG
Statement Reason
1. Given
2. Def. of Isosceles Triangle
3. Midpoint theorem
4. Reflexive property
5. SSS
1
2
3
4
5
Triangle CDE is isosceles
CD = ED
CG = GE
DG = DG
EDGCDG