5-4 Congruent Triangles

Congruent Triangles

An Introduction to Corresponding Parts

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

Congruent figures can be rotations of one another.

Congruent figures can be reflections of one another.

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

∆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.”

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

A X

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

B Y

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

C Z

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

AB XY

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

BC YZ

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

AC XZ

∆DEF is congruent to ∆QRS

D E

F

Q

R

S

∆DEF is congruent to ∆QRS

D E

F

Q

R

S

Corresponding parts of these triangles are congruent.

∆DEF is congruent to ∆QRS

D E

F

Q

R

S

Corresponding parts of these triangles are congruent.

D Q

∆DEF is congruent to ∆QRS

D E

F

Q

R

S

Corresponding parts of these triangles are congruent.

E R

∆DEF is congruent to ∆QRS

D E

F

Q

R

S

Corresponding parts of these triangles are congruent.

F S

∆DEF is congruent to ∆QRS

D E

F

Q

R

S

Corresponding parts of these triangles are congruent.

DE QR

∆DEF is congruent to ∆QRS

D E

F

Q

R

S

Corresponding parts of these triangles are congruent.

DF QS

∆DEF is congruent to ∆QRS

D E

F

Q

R

S

Corresponding parts of these triangles are congruent.

FE SR

Practice Time!

1) Are these shapes congruent? Explain.

1) Are these shapes congruent? Explain.

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

2) Are these shapes congruent? Explain.

2) Are these shapes congruent? Explain.

These shapes are not congruent because they are different sizes.

3) Are these shapes congruent? Explain.

3) Are these shapes congruent? Explain.

These shapes are congruent because they are the same size.

4) ∆BAD is congruent to ∆THE

B A

D E

T H

Name all corresponding parts.

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

5) ∆FGH is congruent to ∆JKL

G

F

H

J

K L

Name all corresponding parts.

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

6) ∆QRS is congruent to ∆BRX

BR

Q

S

X

Name all corresponding parts.

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

7) ∆EFG is congruent to ∆FGH

H

G

F

E

Name all corresponding parts.

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

Slide 1 of 3

Slide 2 of 2

Slide 2 of 2

Slide 2 of 2

Slide 2 of 2

Slide 2 of 2

Slide 2 of 2

Slide 2 of 2

Slide 2 of 2

(over Lesson 5-4)

Slide 2 of 2

(over Lesson 5-4)

In the figure, quadrilateral JIHK quadrilateral QRST.

Find a.

3a4b° 6

30°Q

120°R S

H I

JK

3a = 6 3 3

a = 2

c + 10°T

3a = 6 IH RS

Divide both sides by 3.

In the figure, quadrilateral JIHK quadrilateral QRST.

3a4b° 6

30°Q

120°R S

H I

JK c + 10°

T

Divide both sides by 4. 4 4 4b = 1204b = 120 H S

b = 30°

Find b.

In the figure, quadrilateral JIHK quadrilateral QRST.

Find c.

Subtract 10 from both sides.–10 –10

c + 10 = 30c + 10 = 30 K T

3a4b° 6

30°Q

120°R S

H I

JK c + 10°

T

c = 20°

Congruent Triangles

THE END