1. Similar Figures and Proportions
5-7
Similar Figures and Proportions
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. Insert Lesson Title Here
Course 1
5-6
Customary Measurements
Insert Lesson Title Here
Lesson Quiz: Part II
4. Convert 13 gallons to quarts.
5. Seth is returning from a 5-mile hike. He passes a trail sign that says, “3,520 feet to base camp.” How many more miles does Seth have to hike? 52
2 3

3. Insert Lesson Title Here
Course 2
5-7
Similar Figures and Proportions
Insert Lesson Title Here
Vocabulary
similar
corresponding sides
corresponding angles

4. Similar Figures and Proportions
Course 2
5-7
Similar Figures and Proportions
When naming similar figures, list the letters of the corresponding vertices in the same order. In the previous table ∆ABC ~ ∆DEF.
Writing Math

5. Similar Figures and Proportions
Course 2
5-7
Similar Figures and Proportions
Matching sides of two or more polygons are called corresponding sides, and matching angles are called corresponding angles.
82◦
Corresponding angles D E F
Corresponding sides A B C
55◦
43◦

6. Similar Figures and Proportions
Course 2
5-7
Similar Figures and Proportions
SIMILAR FIGURES
Two figures are similar if
The measures of their corresponding angles are equal.
The ratios of the lengths of the corresponding sides are proportional.

7. Similar Figures and Proportions
Course 2
5-7
Similar Figures and Proportions
A side of a figure can be named by its endpoints, with a bar above. AB
Without the bar, the letters indicate the length of the side.
Reading Math

10. Similar Figures and Proportions
Course 2
5-7
Similar Figures and Proportions
Example 1 E
AB corresponds to DE.
16 in
10 in A C
28 in
BC corresponds to EF.
4 in D
7 in
40 in F
AC corresponds to DF. B AB DE = ? BC EF = ? AC DF
Write ratios using the corresponding sides. 4 16 = ? 7 28 = ? 10 40
Substitute the length of the sides.
Cross Products Test

11. Similar Figures and Proportions
Course 2
5-7
Similar Figures and Proportions
Example 2
Tell whether the figures are similar.
The corresponding angles of the
figures have equal measure.
Write each set of
corresponding sides as a ratio.

12. Finding Unknown Lengths in Similar Figures
Course 2
5-8
Using Similar Figures
Finding Unknown Lengths in Similar Figures
Find the unknown length in similar figures. AC QS = AB QR
Write a proportion using corresponding sides. 12 48 14 w =
Substitute lengths of the sides.
12 · w = 48 · 14
Find the cross product.
12w = 672
Multiply.
12w 12
672 12 =
Divide each side by 12 to isolate the variable.
w = 56
QR is 56 centimeters.

13. Insert Lesson Title Here
Course 2
5-8
Using Similar Figures
Insert Lesson Title Here
Example 1
The inside triangle is similar in shape to the outside triangle. Find the length of the base of the inside triangle.

14. 5-8 Using Similar Figures Example 2
Course 2
5-8
Using Similar Figures
Example 2
City officials want to know the height of a traffic light. Estimate the height of the traffic light.
h ft
27.25 ft
48.75 ft
The traffic light is about 30 feet tall.

15. Insert Lesson Title Here
Course 2
5-8
Using Similar Figures
Insert Lesson Title Here
Lesson Quiz: Part I
Find the unknown length in each pair of similar figures. 1.
x = 120 cm 2.
t = 150 cm