Identify and use properties of congruent polygons

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

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

4. 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 a congruence statement for the congruent
triangles below.
C M
X J
B
F
ΔCMX ≅ ΔFBJ

6. Example: Given ΔTEA ≅ ΔCUP, find x
From the congruence statement, we know that . . So,
2x – 2 = 6
T
E A
C
U
P
2x – 2 53535353°°°°
6
10
TE CU≅
2x – 2 = 6
2x = 8
x = 4