6th Grade Math Textbook, Fundamentals

 &KDSWHU

6-7

Similarity

Objective To determine similarity • To name corresponding parts of similar figures

• To use proportions to find missing dimensions

Is triangle ABCsimilar to triangle DEF?

 have the same shape but may be a different

size. If two figures are similar, all the pairs of corresponding

anglesare congruent, and the ratios of the lengths of all the

pairs of corresponding sidesare equal.

of similar figures are angles that are

in the same relative position. of similar

figures are sides that are in the same relative position.

To determine whether the two triangles are similar:

• Compare the measures of corresponding angles.

Acorresponds to D. 30° 30° AD

Bcorresponds to E. 110° 110° BE

Ccorresponds to F. 40° 40° CF

So the corresponding angles of the two triangles are congruent.

• Compare the ratios of the lengths of corresponding sides.

ABcorresponds to DE. BCcorresponds to EF. ACcorresponds to DF.

  

Each pair of corresponding sides has a ratio 4 : 1. So the

ratios of the lengths of the corresponding sides are equal.

Triangle ABCis similar to triangle DEF since the

corresponding angles are congruent and the ratios of the

corresponding sides are equal.

You can use symbols to show that triangle ABCis similar to triangle DEF.

ABC DEF List the letters in order of the corresponding parts.

Read as:triangle ABCis similar to triangle DEF.

Corresponding angles

Corresponding sides

Similar figures

4

1

24

6

AC

DF

4

1

12

3

BC

EF

AB

DE

4

1

16

4

Remember:Congruent figures have

the same shape and the same size.

Symbols

means “is congruent to.”

ABmeans “side AB.”

ABmeans “the measure of side AB.”

means “is similar to.”

16 cm

24 cm

12 cm

4 cm

6 cm

3 cm

AC

B

DF

E

110°

110°

30° 40° 30° 40°

corresponding sides

corresponding angles