Holt CA Course 1

9-9 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.

Holt CA Course 1

9-9 Congruent Figures

Identify any congruent figures.

A.

Additional Example 1: Identifying Congruent Figures in the Real World

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

Holt CA Course 1

9-9 Congruent Figures

Identify any congruent figures.

B.

Additional Example 1: Identifying Congruent Figures in the Real World

The sectors in the figure are congruent.

Holt CA Course 1

9-9 Congruent Figures

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

Remember!

Holt CA Course 1

9-9 Congruent Figures

Identify any congruent figures.

A.

Check It Out! Example 1

The sides of the figures are are not congruent.

Holt CA Course 1

9-9 Congruent Figures

Identify any congruent figures.

B.

Check It Out! Example 1

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

Holt CA Course 1

9-9 Congruent Figures

If all of the corresponding sides and angles of two polygons are congruent, then the polygons are congruent.

Holt CA Course 1

9-9 Congruent Figures

Determine whether the triangles are congruent.

Additional Example 2: Identifying Congruent Triangles

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.

Holt CA Course 1

9-9 Congruent Figures

Determine whether the triangles are congruent.

Check It Out! Example 2

AC = 8 mAB = 6 mBC = 10 m

DF = 8 mDE = 6 mEF = 10 m

A

B

C F D

E

6 m 6 m

8 m8 m

10 m 10 m

Holt CA Course 1

9-9 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.

Holt CA Course 1

9-9 Congruent Figures

Determine the missing measure in the set of congruent polygons.

A.

Additional Example 3: Using Congruence to Find Missing Measures

The corresponding angles of congruent polygons are congruent.

The missing angle measure is 110°.

Holt CA Course 1

9-9 Congruent Figures

The corresponding sides of congruent polygons are congruent.

The missing side length is 28 mm.

Determine the missing measure in the set of congruent polygons.

B.

Additional Example 3: Using Congruence to Find Missing Measures

Holt CA Course 1

9-9 Congruent FiguresCheck It Out! Example 3

Determine the missing measure in the set of congruent polygons.

A.

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.

?

Holt CA Course 1

9-9 Congruent FiguresCheck It Out! Example 3

Determine the missing measure in the set of congruent polygons.

B.

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°

?