Identify and prove congruent triangles using SSS, SAS, and HL.

1. Congruent Triangles
The student is able to (I can):
• Identify and prove congruent triangles given
— Three pairs of congruent sides (Side-Side-Side)
— Two pairs of congruent sides and a pair of congruent— Two pairs of congruent sides and a pair of congruent
included angles (Side-Angle-Side)
— A Hypotenuse and a Leg of a right triangle

2. SSS – Side-Side-Side
If three sides of one triangle are congruent
to three sides of another triangle, then the
triangles are congruent.
I C P6
T N U
4
6
7 4 7
ΔTIN ≅ ΔCUP

3. Example Given: , D is the midpoint of
Prove: ΔFRD ≅ ΔERD
F
R
ED
FR ER≅ FE
StatementsStatementsStatementsStatements ReasonsReasonsReasonsReasonsStatementsStatementsStatementsStatements ReasonsReasonsReasonsReasons
1. 1. Given
2. D is midpt of 2. Given
3. 3. Def. of midpoint
4. 4. Refl. prop. ≅
5. ΔFRD ≅ ΔERD 5. SSS
FR ER≅
FE
FD ED≅
RD RD≅

4. SAS – Side-Angle-Side
If two sides and the included angle of one
triangle are congruent to two sides and the
included angle of another triangle, then the
triangles are congruent.
H U
L
S
T
A
ΔLHS ≅ ΔUTA

5. Example Given: , A is the midpoint of
Prove: ΔFAR ≅ ΔEAM F
R
A
M
E
FA EA≅ RM
E
StatementsStatementsStatementsStatements ReasonsReasonsReasonsReasons
1. 1. Given
2. ∠FAR ≅ ∠EAM 2. Vertical ∠s
3. A is midpt of 3. Given
4. 4. Def. of midpoint
5. ΔFAR ≅ ΔEAM 5. SAS
FA EA≅
RM
RA MA≅

6. HL – hypotenuse-leg
If the hypotenuse and leg of one right
triangle are congruent to the hypotenuse
and leg of another right triangle, then the
two triangles are congruent.
J
E
M
O
E
AC
∆JOE ≅ ∆MAC