8-9 Congruent Figures

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpFind 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°

50°

Course 2

8-9 Congruent Figures

52°

Problem of the Day

Draw triangles ABC and DEF so thata. AB = DE and BC = EFb. angle A is congruent to angle D.c. the triangles are not congruent.

Course 2

8-9 Congruent Figures

D E

F

A B

C

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

Course 2

8-9 Congruent Figures

Vocabulary

Side-Side-Side Rule

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Course 2

8-9 Congruent Figures

Course 2

8-9 Congruent Figures

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.

Identify any congruent figures.

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

Course 2

8-9 Congruent Figures

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

Identify any congruent figures.

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

Course 2

8-9 Congruent Figures

The sectors in the figure are congruent.

Identify any congruent figures.

Check It Out: Example 1A

Course 2

8-9 Congruent Figures

The sides of the figures are are not congruent.

Identify any congruent figures.

Check It Out: Example 1B

Course 2

8-9 Congruent Figures

The figures are not congruent. The figure on the outside is larger than the one on the inside.

Course 2

8-9 Congruent Figures

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.

Determine whether the triangles are congruent.

Additional Example 2: Identifying Congruent Triangles

Course 2

8-9 Congruent Figures

4 cm6 cm 5 cm

4 cm

4 cm

4 cmA

B

C

R

P

QAB = 4 cmBC = 4 cmAC = 6 cm

PQ = 4 cmPR = 4 cmRQ = 5 cm

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.

Determine whether the triangles are congruent.

Check It Out: Example 2

Course 2

8-9 Congruent Figures

AC = 8 mAB = 6 mBC = 10 m

DF = 8 mDE = 6 mEF = 10 m

The notation ABC is read “triangle ABC.”

Reading Math

A

B

C F D

E

6 m 6 m

8 m8 m

10 m10 m

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.

Course 2

8-9 Congruent Figures

For polygons with more than three sides, it is notenough to compare the measures of their sides.For example, the corresponding sides of the figures below are congruent, but the figures are not congruent.

If you know that two figures are congruent, youcan find the missing measures in the figures.

Determine the missing measure in the set of congruent polygons.

Additional Example 3: Using Congruence to Find Missing Measures

Course 2

8-9 Congruent Figures

The missing angle measure is 110°.

The corresponding parts of congruent polygons are congruent.

The missing side length is 28mm.

Check It Out: Example 3A

Determine the missing measure in the set of congruent polygons.

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Course 2

8-9 Congruent Figures

6 ft

8 ft

5 ft120°135°

60°45°

6 ft

8 ft

5 ft

4 ft

120°135°45°

60°

The missing sidelength is 4 ft.

The correspondingsides are congruent.

?

Check It Out: Example 3B

Determine the missing measure in the set of congruent polygons.

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Course 2

8-9 Congruent Figures

The missing anglemeasure is 130°.

The correspondingangles are congruent.

6 ft

6 ft

8 ft

4 ft

5 ft

5 ft

4 ft

8 ft

10 ft

10 ft

120°130° 110°

100°80°

110°

80°100°

120°?

Lesson Quiz1. Identify any congruent figures.

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Course 2

8-9 Congruent Figures

2. Determine the missing measures in the set of congruent polygons.

none

a =11, b =6, c = 110°