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Ch 9.2. There are 480 sophomores and 520 juniors in a high school. Find the ratio of juniors to sophomores. A strip of wood molding that is 33 inches long is cut into two pieces whose lengths are in the ratio of 7:4. What are the lengths of the two pieces?. 520 480. 13 12. =.

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5 minute check 1

Ch 9.2

There are 480 sophomores and 520 juniors in a high school. Find the ratio of juniors to sophomores.

A strip of wood molding that is 33 inches long is cut into two pieces whose lengths are in the ratio of 7:4. What are the lengths of the two pieces?

520

480

13

12

=

7x + 4x = 33, x = 3; 7(3) = 21 & 4(3) = 12

x = 7

x = 2

x = 3.25

5-Minute Check 1
ch 9 2 similar polygons

Ch 9.2

Learning Target:

I will be able to identify similar polygons and solve problems using the properties of similar polygons.

Standard 4.0

Students prove basic theorems involving similarity.

Ch 9.2Similar Polygons
vocabulary

Ch 9.2

  • polygon – a closed figure in a plane formed by segments called sides.
  • similar polygons – polygons that are the same shape but not necessarily the same size.
  • scale drawing – used to represent something that is too large or too small to be drawn to actual size.
Vocabulary
example 1

Ch 9.2

Use a Similarity Statement

If ΔABC ~ ΔRST, list all pairs of congruent angles and write a proportion that relates the corresponding sides.

Example 1
example 11

Ch 9.2

Use a Similarity Statement

Use the similarity statement.

ΔABC ~ ΔRST

Answer:

Congruent Angles: A R, B S,C T

Example 1
example 12

Ch 9.2

A.HGK  QPR

B.

C.K  R

D.GHK  QPR

If ΔGHK ~ ΔPQR, determine which of the following similarity statements is not true.

Example 1
example 2

Ch 9.2

Identify Similar Polygons

A. MENUSTan is designing a new menu for the restaurant where he works. Determine whether the size for the new menu is similar to the original menu. If so, write the similarity statement and scale factor. Explain your reasoning.

Original Menu: New Menu:

Example 2
example 21

Ch 9.2

Identify Similar Polygons

Step 1 Compare corresponding angles.

Since all angles of a rectangle are right angles and right angles are congruent, corresponding angles are congruent.

Step 2 Compare corresponding sides.

Answer:Since corresponding sides are not proportional, ABCD is not similar to FGHK. So, the menus are not similar.

Example 2
example 22

Ch 9.2

Identify Similar Polygons

B. MENUSTan is designing a new menu for the restaurant where he works. Determine whether the size for the new menu is similar to the original menu. If so, write the similarity statement and scale factor. Explain your reasoning.

Original Menu: New Menu:

Example 2
example 23

Ch 9.2

4

__

5

Identify Similar Polygons

Step 1 Compare corresponding angles.

Since all angles of a rectangle are right angles and right angles are congruent, corresponding angles are congruent.

Step 2 Compare corresponding sides.

Answer:Since corresponding sides are proportional, ABCD ~ RSTU. So, the menus are similar with a scale factor of .

Example 2
example 24

Ch 9.2

A.BCDE ~ FGHI, scale factor =

B.BCDE ~ FGHI, scale factor =

C.BCDE ~ FGHI, scale factor =

D.BCDE is not similar to FGHI.

1

4

3

__

__

__

2

5

8

Original: New:

A. Thalia is a wedding planner who is making invitations. Determine whether the size for the new invitations is similar to the original invitations used. If so, choose the correct similarity statement and scale factor.

Example 2
example 25

Ch 9.2

A.BCDE ~ WXYZ, scale factor =

B.BCDE ~ WXYZ, scale factor =

C.BCDE ~ WXYZ, scale factor =

D.BCDE is not similar to WXYZ.

1

4

3

__

__

__

2

5

8

Original: New:

B. Thalia is a wedding planner who is making invitations. Determine whether the size for the new invitations is similar to the original invitations used. If so, choose the correct similarity statement and scale factor.

Example 2
example 3

Ch 9.2

Use Similar Figures to Find Missing Measures

A.The two polygons are similar. Find x.

Use the congruent angles to write the corresponding vertices in order.

polygon ABCDE ~ polygon RSTUV

Example 3
example 31

Ch 9.2

9

__

2

Answer: x =

Use Similar Figures to Find Missing Measures

Write a proportion to find x.

Similarity proportion

Cross Products Property

Multiply.

Divide each side by 4. Simplify.

Example 3
example 32

Ch 9.2

Use Similar Figures to Find Missing Measures

B.The two polygons are similar. Find y.

Use the congruent angles to write the corresponding vertices in order.

polygon ABCDE ~ polygon RSTUV

Example 3
example 33

Ch 9.2

13

__

3

Answer: y =

Use Similar Figures to Find Missing Measures

Similarity proportion

AB = 6, RS = 4, DE = 8, UV = y + 1

Cross Products Property

Multiply.

Subtract 6 from each side.

Divide each side by 6 and simplify.

Example 3
example 34

Ch 9.2

A. The two polygons are similar. Solve for a.

A.a = 1.4

B.a = 3.75

C.a = 2.4

D.a = 2

Example 3
example 35

Ch 9.2

B. The two polygons are similar. Solve for b.

A. 1.2

B. 2.1

C. 7.2

D. 9.3

Example 3
example 4

Ch 9.2

Use a Scale Factor to Find Perimeter

If ABCDE ~ RSTUV, find the scale factor of ABCDE to RSTUV and the perimeter of each polygon.

Example 4
example 41

Ch 9.2

The scale factor ABCDE to RSTUV is or .

Write a proportion to find the length of DC.

4

__

AE

___

7

VU

Since DC AB and AE  DE, the perimeter of ABCDE is 6 + 6 + 6 + 4 + 4 or 26.

Use a Scale Factor to Find Perimeter

Write a proportion.

4(10.5) = 7 ● DC Cross Products Property

6 = DC Divide each side by 7.

Example 4
example 42

Ch 9.2

Use a Scale Factor to Find Perimeter

Use the perimeter of ABCDE and scale factor to write a proportion. Let x represent the perimeter of RSTUV.

Theorem 7.1

Substitution

4x = (26)(7) Cross Products Property

x = 45.5 Solve.

Answer:The perimeter of ABCDE is 26 and the perimeter of RSTUV is 45.5.

Example 4
example 43

Ch 9.2

If LMNOP ~ VWXYZ, find the perimeter of each polygon.

A.LMNOP = 40, VWXYZ = 30

B.LMNOP = 32, VWXYZ = 24

C.LMNOP = 45, VWXYZ = 40

D.LMNOP = 60, VWXYZ = 45

Example 4
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