I can use scale factors to determine of two shapes are similar, and solve for lengths. HW: Page 473, #9-23 odd, 27, 28, 47

Concept

Example 1

Use a Similarity Statement

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

Example 1

Use a Similarity Statement

Use the similarity statement.

ΔABC ~ ΔRST

Congruent Angles: ∠A ≅ ∠R, ∠B ≅ ∠S, ∠C ≅ ∠T

Answer:

Scale Factor – Ratio of One Shape to Another

If all sides do not have the same scale factor, then the shape is not similar. If all the corresponding angles are not congruent, then the shape is not similar.

Example 2

Identify Similar Polygons

A. MENUS Tan 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

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

Identify Similar Polygons

B. MENUS Tan 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

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 . __ 4 5

Example 3

Use Similar Figures to Find Missing Measures

A. The two polygons are similar. Find x and y

Example 3

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

Concept

Example 4

Use a Scale Factor to Find Perimeter

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

The scale factor ABCDE to RSTUV is or . ___ AE VU

__ 4 7

Example 4

Use a Scale Factor to Find Perimeter

Write a proportion to find the length of DC.

Perimeter of ABCDE is 6 + 6 + 6 + 4 + 4 = 26.

4(10.5) = 7 ● DC 6 = DC

In order to Find either Perimeter , we need to more information

Example 4

Use a Scale Factor to Find Perimeter

Use the perimeter of ABCDE and scale factor to write a proportion.

4x = (26)(7)

x = 45.5

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

Example 4

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

•  HW Time

•  HW: Page 473, #9-23 odd, 27, 28, 47