1. I can use proportions to find missing measures in similar figures

2. Vocabulary
corresponding sides
corresponding angles
similar

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

4. Similar figures have the same shape but not necessarily the same size.
Two figures are similar if
• the measures of the corresponding angles are equal.
• the ratios of the lengths of the corresponding sides t are proportional.
Similar Figures

5. (Not exactly the same, but pretty close!)
Similar Figures
(Not exactly the same, but pretty close!)

6. Finding Missing Measures in Similar Figures
The two triangles are similar. Find the missing length y and the measure of D.

7. The width of the actual painting is 81 cm.
This reduction is similar to a picture that Katie painted. The height of the actual painting is 54 centimeters. What is the width of the actual painting?
The width of the actual painting is 81 cm.

8. The width of the actual painting is 52 inches.
This reduction is similar to a picture that Marty designed. The height of the actual picture is 39 inches. What is the width of the actual picture?
4 in.
3 in.
The width of the actual painting is 52 inches.

9. Lesson Quiz for Student Response Systems
1. These two triangles are similar. Identify the missing length x.
A. 3 cm
B. 4 cm
C. 5 cm
D. 6 cm

10. Lesson Quiz for Student Response Systems
2. These two triangles are similar. Identify the measure R.
A. 30
B. 50
C. 80
D. 90

11. Lesson Quiz for Student Response Systems
3. These two triangles are similar. Identify the missing length y.
A. 27 in.
B. 21 in.
C. 9 in.
D. 8 in.

12. A carpenter is making a rectangular table top of dimensions 9 ft by 12 ft. However, he is going to increase its size proportionally. If the width is to be 15 ft, what will the length be?
A. 24 ft
B. 20 ft
C. 18 ft
D. 12 ft

13. I can use proportions and similar figures to find unknown measurements
7.5 Indirect Measurement
I can use proportions and similar figures to find unknown measurements

14. Use the similar triangles to find the height of the tree.
The tree is 21 feet tall.

15. A rocket casts a shadow that is 91. 5 feet long
A rocket casts a shadow that is 91.5 feet long. A 4-foot model rocket casts a shadow that is 3 feet long. How tall is the rocket?
The rocket is 122 feet tall.

16. On a sunny afternoon, a goalpost casts a 75 ft shadow. A 6
On a sunny afternoon, a goalpost casts a 75 ft shadow. A 6.5 ft football player next to the goal post has a shadow 19.5 ft long. How tall is the goalpost?
25 feet

17. On a sunny afternoon, a tree casts a 120-foot shadow
On a sunny afternoon, a tree casts a 120-foot shadow. A 6-foot man beside the tree has a shadow 36 feet long. How tall is the tree?
A. 20 ft
B. 30 ft
C. 36 ft
D. 60 ft