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7-9. Congruent Figures. Course 2. Warm Up. Problem of the Day. Lesson Presentation. 7-9. Congruent Figures. Course 2. Warm Up Find the measure of the third angle in the triangle, given two angle measures. 1. 58°, 104° 2. 32°, 63° 3. 90°, 38° 4. 42°, 88°. 18°. 85°. 52°. 50°.

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7-9

Congruent Figures

Course 2

Warm Up

Problem of the Day

Lesson Presentation

7-9

Congruent Figures

Course 2

Warm Up

Find the measure of the third angle in the triangle, given two angle measures.

1.58°, 104°

2. 32°, 63°

3. 90°, 38°

4. 42°, 88°

18°

85°

52°

50°

7-9

Congruent Figures

C

F

D

E

A

B

Course 2

Problem of the Day

Draw triangles ABC and DEF so that

a.AB = DE and BC = EF

b. angle A is congruent to angle D.

c. the triangles are not congruent.

7-9

Congruent Figures

Course 2

Learn to identify congruent figures and to use congruence to solve problems.

7-9

Congruent Figures

Course 2

Insert Lesson Title Here

Vocabulary

Side-Side-Side Rule

7-9

Congruent Figures

Course 2

Which center circle do you think is bigger? In spite of appearances, the two center circles are congruent. Their apparent differences are optical illusions. One way to determine whether figures are congruent is to see if one

figure will fit exactly over the other one.

Look at the two patterns.

7-9

Congruent Figures

Course 2

Additional Example 1A: Identifying Congruent Figures in the Real World

Identify any congruent figures.

A.

The sides of the octagons are not congruent. Each side of the outer figure is larger than each side of the inner figure.

7-9

Congruent Figures

Course 2

Additional Example 1B: Identifying Congruent Figures in the Real World

Identify any congruent figures.

B.

The buttons labeled 1, 4, 7, and * are congruent. The buttons labeled 2, 5, 8, and 0 are also congruent. Also the buttons labeled 3, 6, 9, and # are congruent.

7-9

Congruent Figures

Course 2

If all of the corresponding sides and angles of two polygons are congruent, then the polygons are congruent. For triangles in particular, the corresponding angles will always be congruent if the corresponding sides are congruent. This is called the Side-Side-Side Rule. Because of this rule, when determining whether triangles are congruent, you only need to determine whether the sides are congruent.

7-9

Congruent Figures

Course 2

Additional Example 2: Identifying Congruent Triangles

Determine whether the triangles are congruent.

Q

C

4 cm

4 cm

AB = 4 cm

BC = 4 cm

AC = 6 cm

PQ = 4 cm

PR = 4 cm

RQ = 5 cm

B

P

5 cm

6 cm

4 cm

4 cm

R

A

The triangles are not congruent. Although two sides in one triangle are congruent to two sides in the other, the third sides are not congruent.

7-9

Congruent Figures

By the Side-Side-Side Rule, ABC is congruent to DEF, or

ABCDEF. If you flip one triangle, it will fit exactly over the other.

The notation ABC is read “triangle ABC.”

Course 2

Try This: Example 2

Determine whether the triangles are congruent.

AC = 8 m

AB = 6 m

BC = 10 m

DF = 8 m

DE = 6 m

EF = 10 m

B

E

10 m

10 m

6 m

6 m

A

C

D

F

8 m

8 m

7-9

Congruent Figures

120 m

120 m

70 m

70 m

70 m

70 m

120 m

120 m

Course 2

For polygons with more than three sides, it is not

enough to compare the measures of their sides.

For example, the corresponding sides of the

figures below are congruent, but the figures are

not congruent.

145°

35°

35°

145°

If you know that two figures are congruent, you

can find the missing measures in the figures.

7-9

Congruent Figures

Course 2

Additional Example 3A: Using Congruence to Find Missing Measures

Determine the missing measures in the set of congruent polygons.

The corresponding

sides are congruent.

The missing side measure is 28 mm.

7-9

Congruent Figures

Course 2

Additional Example 3B: Using Congruence to Find Missing Measures

Determine the missing measure in the set of congruent polygons.

The corresponding angles are congruent.

The missing angle measure is 88°.

7-9

Congruent Figures

Course 2

Insert Lesson Title Here

Try This: Example 3A

Determine the missing measure in the set of congruent polygons.

135°

5 ft

The corresponding

sides are congruent.

120°

6 ft

45°

60°

8 ft

The missing side

measure is 4 ft.

8 ft

60°

45°

6 ft

135°

5 ft

120°

4 ft

7-9

Congruent Figures

Course 2

Insert Lesson Title Here

Try This: Example 3B

Determine the missing measure in the set of congruent polygons.

6 ft

5 ft

130°

110°

8 ft

The corresponding

angles are congruent.

120°

80°

4 ft

100°

10 ft

The missing angle

measure is 130°.

10 ft

100°

4 ft

80°

120°

8 ft

110°

?

5 ft

6 ft

7-9

Congruent Figures

D

A

5 cm

5 cm

7 cm

8 cm

E

8 cm

B

8 cm

C

F

Course 2

Insert Lesson Title Here

Lesson Quiz

no

1. Are the triangles congruent?

2. Determine the missing measures for the

set of congruent polygons.

11

70°

70°

110°

c

6

6

6

b

70°

70°

110°

110°

18

a

a =11, b =6, c = 110°