Two triangles are congruent if their corresponding angles are equal and their corresponding sides are equal. The order of the vertices in a congruence statement indicates the matching parts between the triangles. If two triangles are congruent, then their corresponding parts will be equal.

1. Congruent Triangles
The student is able to (I can):
• Use properties of congruent triangles
• Prove triangles congruent using the definition of
congruence.

2. Congruent Triangles
Geometric figures are congruent if they are the same sizesizesizesize
and shapeshapeshapeshape. Corresponding angles and corresponding
sides are in the same position in polygons with the same
number of sides.

3. congruent
polygons
Two or more polygons whose corresponding
angles and sides are congruent.
E D
R A
P
C
Corresponding
Angles
∠R ≅ ∠C
∠E ≅ ∠A
∠D ≅ ∠P
Corresponding
Sides
≅RD CP
≅RE CA
≅ED AP
Thus, ΔRED ≅ ΔCAP.

4. Note: 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
Example: Name the corresponding sides if
ΔTAN ≅ ΔCOS.
TA CO; AN OS;NT SC≅ ≅ ≅

5. Example: Write the congruence statement
for the congruent triangles below.
C M
X J
B
F
∆CMX ≅ ∆FBJ

6. Example: Given ΔTEA ≅ ΔCUP, find x
From the congruence statement, we know
that TE ≅ CU. So,
2x — 2 = 6
2x = 8
x = 4
T
E A
C
U
P
2x — 2 53º53º53º53º
6
10