Write and interpret congruence statements Use properties of congruent polygons to solve problems

1. Congruent Polygons
The student is able to (I can):
• Write and interpret congruence statements
• Use properties of congruent triangles
• Prove polygons 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.
congruent polygonscongruent polygonscongruent polygonscongruent polygons – two or more polygons whose
corresponding angles and sides are congruent.

3. 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. In a congruence statement, the order of the vertices
indicates the corresponding parts.
Example: Name the corresponding angles if
SWIM ≅ 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

6. Example: Write a congruence statement for the congruent
triangles below.
Answer: The easiest way to do this is to match the angle
markings: ∠C ≅∠F, etc. Thus, ΔCMX ≅ ΔFBJ
C M
X J
B
F

7. Example: Given ΔTEA ≅ ΔCUP, find x
T
E A
C
U
P
2x – 2
6
10

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