similar figures and_proportions

Similar Figures and Proportions

Warm UpWarm UpProblem of the DayProblem of the DayLesson PresentationLesson Presentation

Warm UpFind the cross products, then tell whether the ratios are equal.

Course 2

5-7 Similar Figures and Proportions

1. 166

, 4015

2. 38

, 1846

3. 89

, 2427

4. 2812

, 4218

240 = 240; equal

216 = 216; equal

504 = 504; equal

138 = 144; not equal

Problem of the DayEvery 8th telephone pole along a road has a red band painted on it. Every 14th pole has an emergency call phone on it. What is the number of the first pole with both a red band and a call phone? 56

Course 2


Learn to use ratios to determine if two figures are similar.

Course 2


Vocabularysimilarcorresponding sidescorresponding angles

Insert Lesson Title Here

Course 2


Course 2


Octahedral fluorite is a crystal found in nature. It grows in the shape of an octahedron, which is a solid figure with eight triangular faces. The triangles in different-sized fluorite crystals are similar figures. Similar figures have the same shape but not necessarily the same size.

Course 2


When naming similar figures, list the letters of the corresponding vertices in the same order. In the previous table ∆ABC ~ ∆DEF.

Writing Math

Course 2


Matching sides of two or more polygons are called corresponding sides, and matching angles are called corresponding angles.

82◦

Corresponding angles

D

E

F

Corresponding sides

A

B

C

82◦

55◦43◦ 55◦43◦

Course 2


SIMILAR FIGURESTwo figures are similar if• The measures of their corresponding angles are

equal. • The ratios of the lengths of the corresponding

sides are proportional.

Course 2


A side of a figure can be named by its endpoints, with a bar above.

AB

Without the bar, the letters indicate the length of the side.

Reading Math

Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar.

Additional Example 1: Determining Whether Two Triangles Are Similar

Course 2


A C

B

10 in4 in 7 in D

E

F

16 in 28 in

40 in

AB corresponds to DE.BC corresponds to EF.

ABDE =? BC

EF =? ACDF

416

728

1040

14

14

14

Since the ratios of the corresponding sides are equivalent, the triangles are similar.

Write ratios using the corresponding sides.

Substitute the length of the sides.

Simplify each ratio.

=? =?

AC corresponds to DF.

=? =?

Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar.

Check It Out: Example 1

Course 2


A C

B

9 in3 in 7 in D

E

F

9 in 21 in

27 in

AB corresponds to DE.BC corresponds to EF.

ABDE =? BC

EF =? ACDF

39

721

927

13

13

13

Since the ratios of the corresponding sides are equivalent, the triangles are similar.

Write ratios using the corresponding sides.



=? =?

AC corresponds to DF.

=? =?

Tell whether the figures are similar.

Additional Example 2: Determining Whether Two Four-Sided Figures are Similar

Course 2


The corresponding angles of the figures have equal measure.

Write each set of corresponding sides as a ratio.

Additional Example 2 Continued

Course 2


MNQR MN corresponds to QR.

NORS

OPST

MPQT

NO corresponds to RS.

OP corresponds to ST.

MP corresponds to QT.

Determine whether the ratios of the lengths of the corresponding sides are proportional.

Additional Example 2 Continued

Course 2


Write ratios using corresponding sides.



Since the ratios of the corresponding sides are equivalent, the figures are similar.

MNQR

=? NORS

=? OPST

=? MPQT

6 9=? 8

12 =? 4 6 =? 10

15

23 = 2

3 = 23 = 2

3? ? ?

Tell whether the figures are similar.

Check It Out: Example 2

Course 2


The corresponding angles of the figures have equal measure.

100 m

80 m

60 m 47.5 m80°

90° 125°65°

M P

NO

400 m

320 m

190 m240 m

80° 65°

90° 125°

Q T

R S

Write each set of corresponding sides as a ratio.

Check It Out: Example 2 Continued

Course 2


MNQR MN corresponds to QR.

NORS

OPST

MPQT

NO corresponds to RS.

OP corresponds to ST.

MP corresponds to QT.

100 m

80 m

60 m 47.5 m80°

90° 125°65°

M P

NO

400 m

320 m

190 m240 m

80° 65°

90° 125°

Q T

R S

Determine whether the ratios of the lengths of the corresponding sides are proportional.

Check It Out: Example 2 Continued

Course 2


Write ratios using correspondingsides.



Since the ratios of the corresponding sides are equivalent, the figures are similar.

100 m

80 m

60 m 47.5 m80°

90° 125°65°

M P

NO

400 m

320 m

190 m240 m

80° 65°

90° 125°

Q T

R S

MNQR

=? NORS

=? OPST

=? MPQT

60240 =? 80

320 =? 47.5190 = ? 100

400

14 = 1

4 = 14 = 1

4? ? ?

Lesson Quiz: Part I


Course 2


Tell whether the figures are similar.1. similar59°

59°

35°35°

86°86°

Lesson Quiz: Part II


Course 2


Tell whether the figures are similar.2.

not similar

119°

55°

107°

79°

107°

80°

135°

38°

similar figures and_proportions

Education