1. Warm Up

2. Warm Up Solve each proportion. = = 1. b = 10 2. y = 8 = = 3. 4. m = 5230 3 9 = 56 35 y 5 = 1.
b = 10 2.
y = 8 4 12 p 9 = 56 m 28 26 = 3. 4.
m = 52
p = 3

3. Student Learning Targets
TN State Standard: 8.G.A.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the
angle-angle criterion for similarity of triangles.
Student Learning Targets
Future Target
I will transform plane figures using translations, rotations, and reflections
Present Target
I will determine whether figures are similar
and find missing dimensions in similar figures.
Past Target
I can use properties of congruent figures to solve problems.

4. Vocabulary
similar
corresponding sides
corresponding angles

5. Similar figures have the same shape, but not necessarily the same size.
Corresponding sides of two figures are in the same relative position, and corresponding angles are in the same relative position. Two figures are similar if the lengths of corresponding sides are proportional and the corresponding angles have equal measures.

7. Additional Example 1: Identifying Similar Figures
Which rectangles are similar?
Since the three figures are all rectangles, all the angles are right angles. So the corresponding angles are congruent.

8. Additional Example 1 Continued
Compare the ratios of corresponding sides to see if they are equal.
length of rectangle J
length of rectangle K
width of rectangle J
width of rectangle K 10 5 4 2 ? =
20 = 20
The ratios are equal. Rectangle J is similar to rectangle K. The notation J ~ K shows similarity.
length of rectangle J
length of rectangle L
width of rectangle J
width of rectangle L 10 12 4 5 ? =
50  48
The ratios are not equal. Rectangle J is not similar to rectangle L. Therefore, rectangle K is not similar to rectangle L.

9. Additional Example 2: Finding Missing Measures in Similar Figures
A picture 10 in. tall and 14 in. wide is to be scaled to 1.5 in. tall to be displayed on a Web page. How wide should the picture be on the Web page for the two pictures to be similar?
Set up a proportion. Let w be the width of the picture on the Web page.
width of a picture
width on Web page
height of picture
height on Web page 14 w = 10
1.5
14 ∙ 1.5 = w ∙ 10
Find the cross products.
21 = 10w
10w 10 21 =
Divide both sides by 10.
2.1 = w
The picture on the Web page should be 2.1 in. wide.

10. Additional Example 3: Using Equivalent Ratios to Find Missing Dimensions
A T-shirt design includes an isosceles triangle with side lengths 4.5 in, 4.5 in., and 6 in. An advertisement shows an enlarged version of the triangle with two sides that are each 3 ft. long. What is the length of the third side of the triangle in the advertisement?
6 in.
x ft
4.5 in.
3 ft =
Set up a proportion.
4.5 • x = 3 • 6
Find the cross products.

11. Additional Example 3 Continued
Multiply.
x = = 4 18
4.5
Solve for x.
The third side of the triangle is 4 ft long.

12. Which rectangles are similar?
Check It Out: Example 1
Which rectangles are similar?
8 ft A
6 ft B C
5 ft
4 ft
3 ft
2 ft
Since the three figures are all rectangles, all the angles are right angles. So the corresponding angles are congruent.

13. Check It Out: Example 1 Continued
Compare the ratios of corresponding sides to see if they are equal.
length of rectangle A
length of rectangle B
width of rectangle A
width of rectangle B 8 6 4 3 ? =
24 = 24
The ratios are equal. Rectangle A is similar to rectangle B. The notation A ~ B shows similarity.
length of rectangle A
length of rectangle C
width of rectangle A
width of rectangle C 8 5 4 2 ? =
16  20
The ratios are not equal. Rectangle A is not similar to rectangle C. Therefore, rectangle B is not similar to rectangle C.

14. Check It Out: Example 2
A painting 40 in. long and 56 in. wide is to be scaled to 10 in. long to be displayed on a poster. How wide should the painting be on the poster for the two pictures to be similar?
Set up a proportion. Let w be the width of the painting on the Poster.
width of a painting
width of poster
length of painting
length of poster 56 w = 40 10
56 ∙ 10 = w ∙ 40
Find the cross products.
560 = 40w
40w 40
560 =
Divide both sides by 40.
14 = w
The painting displayed on the poster should be 14 in. long.

15. Check It Out: Example 3
A flag in the shape of an isosceles triangle with side lengths 18 ft, 18 ft, and 24 ft is hanging on a pole outside a campground. A camp t-shirt shows a smaller version of the triangle with two sides that are each 4 in. long. What is the length of the third side of the triangle on the t-shirt?
24 ft
x in.
18 ft
4 in. =
Set up a proportion.
18 • x = 24 • 4
Find the cross products.

16. Check It Out: Example 3 Continued
Multiply.
x =  5.3 96 18
Solve for x.
The third side of the triangle is about 5.3 in. long.

17. Exit Ticket 17 17

18. Exit Ticket
Use the properties of similar figures to answer each question.
1. A rectangular house is 32 ft wide and 68 ft long. On a blueprint, the width is 8 in. Find the length on the blueprint.
17 in.
2. Karen enlarged a 3 in. wide by 5 in. tall photo into a poster. If the poster is 2.25 ft wide, how tall is it?
3.75 ft
3. Which rectangles are similar?
A and B are similar.