Identify congruent parts based on a congruence relationship statement Identify and prove congruent triangles given Three pairs of congruent sides (Side-Side-Side) Two pairs of congruent sides and a pair of congruent included angles (Side-Angle-Side)

1. Obj. 17 Congruent Triangles
The student is able to (I can):
• Identify congruent parts based on a congruence
relationship statement
• Identify and prove congruent triangles given
— Three pairs of congruent sides (Side-Side-Side)
— Two pairs of congruent sides and a pair of congruent
included angles (Side-Angle-Side)

2. Geometric figures are congruent if they are
the same size and shape Corresponding
shape.
angles and corresponding sides are in the
same position in polygons with the same
number of sides.
congruent
polygons
Two or more polygons whose corresponding
angles and sides are congruent. In a
congruence statement, the order of the
vertices indicates the corresponding parts.
Example: Name the corresponding angles if
polygon SWIM ≅ polygon ZERO.
∠S ≅ ∠Z; ∠W ≅ ∠E; ∠I ≅ ∠R; ∠M ≅ ∠O

3. Example
R
E
C
P
D
A
Corresponding
Angles
Corresponding
Sides
∠R ≅ ∠C
ED ≅ PA
∠E ≅ ∠P
RE ≅ CP
∠D ≅ ∠A
RD ≅ CA
Thus, ΔRED ≅ ΔCPA.

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

5. Example
Given: FR ≅ ER , D is the midpoint of FE
R
Prove: FRD ≅ ERD
F
Statements
1.
2.
3.
4.
FR ≅ ER
D is midpt of FE
FD ≅ ED
RD ≅ RD
5. FRD ≅ ERD
D
Reasons
1. Given
2. Given
3. Def. of midpoint
4. Refl. prop. ≅
5. SSS
E

6. Side-AngleSide
Congruence
Theorem
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
T
S
L
A
ΔLHS ≅ ΔUTA

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