2. Main Idea and New Vocabulary Key Concept: Similar Polygons
Example 1: Identify Similar Polygons
Example 2: Find Missing Measures
Key Concept: Ratios of Similar Figures
Example 3: Find Perimeter
Lesson Menu

3. Identify similar polygons and find missing measures of similar polygons.
corresponding parts
scale factor
Main Idea/Vocabulary

4. Key Concept

5. Identify Similar Polygons
Determine whether triangle DEF is similar to triangle HJK. Explain.
First, check to see if corresponding angles are congruent.
D  H, E  J, and F  K, so all corresponding angles are congruent.
Example 1

6. Identify Similar Polygons
Next, check to see if corresponding sides are proportional.
Since , the corresponding sides are proportional.
Answer: Therefore, the triangles are similar.
Example 1

7. Determine whether the figures are similar. Explain.
A. Yes; corresponding angles are congruent and corresponding sides are proportional.
B. Yes; corresponding angles are congruent and corresponding sides are congruent.
C. No; corresponding angles are congruent, but corresponding sides are not proportional.
D. No; corresponding angles are congruent, but corresponding sides are not congruent.
Example 1 CYP

8. Find the scale factor from rectangle LMNO to rectangle GHIJ.
Find Missing Measures
GEOMETRY Given that rectangle LMNO ~ rectangle GHIJ, find the missing measure.
Find the scale factor from rectangle LMNO to rectangle GHIJ.
scale factor:
Example 2

9. Find Missing Measures
So, a length on rectangle LMNO is times as long as the corresponding length on rectangle GHIJ. Let m represent the measure of ON.
Write the equation.
m = 6 Multiply.
Answer: m = 6
Example 2

10. GEOMETRY Given that quadrilateral KLMN ~ quadrilateral RSTU, find the missing measure.
B. 8
C. 10
D. 12
Example 2 CYP

11. Key Concept 3

12. Convert feet to inches and divide out units.
Find Perimeter
BILLBOARDS A model of a billboard has a side length of 3 inches. The corresponding side on the actual billboard is 4 feet long. The model has a perimeter of 42 inches. What is the perimeter of the actual billboard?
Step 1 The actual length is proportional to the length of the model with a ratio of Find the scale factor.
Convert feet to inches and divide out units.
Example 3

13. Step 2 Find the perimeter of the actual billboard.
Find Perimeter
Step 2 Find the perimeter of the actual billboard.
P = 42 • 16 or 672 Substitute Then simplify.
perimeter of billboard = perimeter of model • scale factor
Answer: The perimeter of the actual billboard is inches or 56 feet.
Example 3

14. PHOTOGRAPHS A photograph has a side length of 8 inches
PHOTOGRAPHS A photograph has a side length of 8 inches. The photo is enlarged to poster size and the corresponding side on the poster is 2 feet long. The photograph has a perimeter of 36 inches. What is the perimeter of the poster?
A. 4 feet
B. 4.5 feet
C. 9 feet
D. 18 feet
Example 3 CYP