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Congruent Triangles
The student is able to (I can):
• Use properties of congruent triangles
• Prove triangles congruent using the definition of
congruence.
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.
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.
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≅ ≅ ≅
Example: Write the congruence statement
for the congruent triangles below.
C M
X J
B
F
∆CMX ≅ ∆FBJ
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

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2.6.1 Congruent Triangles

  • 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