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Page 1: Congruent Triangles

Congruent Triangles

An Introduction to Corresponding Parts

Page 2: Congruent Triangles

Two figures are congruent if they are the same size and same shape.

Page 3: Congruent Triangles

Congruent figures can be rotations of one another.

Page 4: Congruent Triangles

Congruent figures can be reflections of one another.

Page 5: Congruent Triangles

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Page 6: Congruent Triangles

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

Page 7: Congruent Triangles

∆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.”

Page 8: Congruent Triangles

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

A X

Page 9: Congruent Triangles

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

B Y

Page 10: Congruent Triangles

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

C Z

Page 11: Congruent Triangles

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

AB XY

Page 12: Congruent Triangles

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

BC YZ

Page 13: Congruent Triangles

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

AC XZ

Page 14: Congruent Triangles

∆DEF is congruent to ∆QRS

D E

F

Q

R

S

Page 15: Congruent Triangles

∆DEF is congruent to ∆QRS

D E

F

Q

R

S

Corresponding parts of these triangles are congruent.

Page 16: Congruent Triangles

∆DEF is congruent to ∆QRS

D E

F

Q

R

S

Corresponding parts of these triangles are congruent.

D Q

Page 17: Congruent Triangles

∆DEF is congruent to ∆QRS

D E

F

Q

R

S

Corresponding parts of these triangles are congruent.

E R

Page 18: Congruent Triangles

∆DEF is congruent to ∆QRS

D E

F

Q

R

S

Corresponding parts of these triangles are congruent.

F S

Page 19: Congruent Triangles

∆DEF is congruent to ∆QRS

D E

F

Q

R

S

Corresponding parts of these triangles are congruent.

DE QR

Page 20: Congruent Triangles

∆DEF is congruent to ∆QRS

D E

F

Q

R

S

Corresponding parts of these triangles are congruent.

DF QS

Page 21: Congruent Triangles

∆DEF is congruent to ∆QRS

D E

F

Q

R

S

Corresponding parts of these triangles are congruent.

FE SR

Page 22: Congruent Triangles

Practice Time!

Page 23: Congruent Triangles

1) Are these shapes congruent? Explain.

Page 24: Congruent Triangles

1) Are these shapes congruent? Explain.

These shapes are congruent because they are both parallelograms of equal size.

Page 25: Congruent Triangles

2) Are these shapes congruent? Explain.

Page 26: Congruent Triangles

2) Are these shapes congruent? Explain.

These shapes are not congruent because they are different sizes.

Page 27: Congruent Triangles

3) Are these shapes congruent? Explain.

Page 28: Congruent Triangles

3) Are these shapes congruent? Explain.

These shapes are congruent because they are the same size.

Page 29: Congruent Triangles

4) ∆BAD is congruent to ∆THE

B A

D E

T H

Name all corresponding parts.

Page 30: Congruent Triangles

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

Page 31: Congruent Triangles

5) ∆FGH is congruent to ∆JKL

G

F

H

J

K L

Name all corresponding parts.

Page 32: Congruent Triangles

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

Page 33: Congruent Triangles

6) ∆QRS is congruent to ∆BRX

BR

Q

S

X

Name all corresponding parts.

Page 34: Congruent Triangles

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

Page 35: Congruent Triangles

7) ∆EFG is congruent to ∆FGH

H

G

F

E

Name all corresponding parts.

Page 36: Congruent Triangles

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

Page 37: Congruent Triangles

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.

Page 38: Congruent Triangles

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.

Page 39: Congruent Triangles

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°

Page 40: Congruent Triangles

Congruent Triangles

THE END


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