Download - Congruent Triangles
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Congruent Triangles
An Introduction to Corresponding Parts
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Two figures are congruent if they are the same size and same shape.
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Congruent figures can be rotations of one another.
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Congruent figures can be reflections of one another.
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∆ABC is congruent to ∆XYZ
A B
C
X Y
Z
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∆ABC is congruent to ∆XYZ
A B
C
X Y
Z
Corresponding parts of these triangles are congruent.
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∆ABC is congruent to ∆XYZ
A B
C
X Y
Z
Corresponding parts of these triangles are congruent.
Corresponding parts are angles and sides that “match.”
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∆ABC is congruent to ∆XYZ
A B
C
X Y
Z
Corresponding parts of these triangles are congruent.
A X
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∆ABC is congruent to ∆XYZ
A B
C
X Y
Z
Corresponding parts of these triangles are congruent.
B Y
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∆ABC is congruent to ∆XYZ
A B
C
X Y
Z
Corresponding parts of these triangles are congruent.
C Z
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∆ABC is congruent to ∆XYZ
A B
C
X Y
Z
Corresponding parts of these triangles are congruent.
AB XY
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∆ABC is congruent to ∆XYZ
A B
C
X Y
Z
Corresponding parts of these triangles are congruent.
BC YZ
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∆ABC is congruent to ∆XYZ
A B
C
X Y
Z
Corresponding parts of these triangles are congruent.
AC XZ
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∆DEF is congruent to ∆QRS
D E
F
Q
R
S
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∆DEF is congruent to ∆QRS
D E
F
Q
R
S
Corresponding parts of these triangles are congruent.
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∆DEF is congruent to ∆QRS
D E
F
Q
R
S
Corresponding parts of these triangles are congruent.
D Q
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∆DEF is congruent to ∆QRS
D E
F
Q
R
S
Corresponding parts of these triangles are congruent.
E R
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∆DEF is congruent to ∆QRS
D E
F
Q
R
S
Corresponding parts of these triangles are congruent.
F S
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∆DEF is congruent to ∆QRS
D E
F
Q
R
S
Corresponding parts of these triangles are congruent.
DE QR
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∆DEF is congruent to ∆QRS
D E
F
Q
R
S
Corresponding parts of these triangles are congruent.
DF QS
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∆DEF is congruent to ∆QRS
D E
F
Q
R
S
Corresponding parts of these triangles are congruent.
FE SR
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Practice Time!
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1) Are these shapes congruent? Explain.
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1) Are these shapes congruent? Explain.
These shapes are congruent because they are both parallelograms of equal size.
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2) Are these shapes congruent? Explain.
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2) Are these shapes congruent? Explain.
These shapes are not congruent because they are different sizes.
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3) Are these shapes congruent? Explain.
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3) Are these shapes congruent? Explain.
These shapes are congruent because they are the same size.
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4) ∆BAD is congruent to ∆THE
B A
D E
T H
Name all corresponding parts.
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4) ∆BAD is congruent to ∆THE
B A
D E
T H
Name all corresponding parts.
ANGLES SIDES
BA TH AD HE DB ET
B T
A H
D E
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5) ∆FGH is congruent to ∆JKL
G
F
H
J
K L
Name all corresponding parts.
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5) ∆FGH is congruent to ∆JKL
G
F
H
J
K L
Name all corresponding parts.
ANGLES SIDES
FG JK GH KL HF LJ
F J
H L
G K
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6) ∆QRS is congruent to ∆BRX
BR
Q
S
X
Name all corresponding parts.
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6) ∆QRS is congruent to ∆BRX
BR
Q
S
X
Name all corresponding parts.
ANGLES SIDES
QR BR QS BX SR XR
Q B
S X
R R
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7) ∆EFG is congruent to ∆FGH
H
G
F
E
Name all corresponding parts.
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7) ∆EFG is congruent to ∆FGH
H
G
F
E
Name all corresponding parts.
ANGLES SIDES
EF HF EG HG GF GF
E H
F F
G G
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In the figure, quadrilateral JIHK quadrilateral QRST.
Find a.
3a
4b° 6
30°Q
120°R S
H I
J
K
3a = 6 3 3
a = 2
c + 10°
T
3a = 6 IH RS
Divide both sides by 3.
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In the figure, quadrilateral JIHK quadrilateral QRST.
3a
4b° 6
30°Q
120°R S
H I
J
K c + 10°
T
Divide both sides by 4. 4 4 4b = 120
4b = 120 H S
b = 30°
Find b.
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In the figure, quadrilateral JIHK quadrilateral QRST.
Find c.
Subtract 10 from both sides.–10 –10
c + 10 = 30
c + 10 = 30 K T
3a
4b° 6
30°Q
120°R S
H I
J
K c + 10°
T
c = 20°
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Congruent Triangles
THE END