1. Using Proportional Relationships
7-5
Using Proportional Relationships
Holt McDougal Geometry
Holt Geometry

2. Warm Up
Convert each measurement.
1. 6 ft 3 in. to inches
2. 5 m 38 cm to centimeters
Find the perimeter and area of each polygon.
3. square with side length 13 cm
4. rectangle with length 5.8 m and width 2.5 m

3. Whenever dimensions are given in both feet and inches, you must convert them to either feet or inches before doing any calculations.
Helpful Hint

4. Tyler wants to find the height of a telephone pole
Tyler wants to find the height of a telephone pole. He measured the pole’s shadow and his own shadow and then made a diagram. What is the height h of the pole?

5. A student who is 5 ft 6 in. tall measured shadows to find the height LM of a flagpole. What is LM?

6. A scale drawing represents an object as smaller than or larger than its actual size.
The drawing’s scale is the ratio of any length in the drawing to the corresponding actual length.
For example, on a map with a scale of 1 cm:1500 m, one centimeter on the map represents 1500 m in actual distance.

7. On a Wisconsin road map, Kristin measured a distance of 11 in
On a Wisconsin road map, Kristin measured a distance of 11 in. from Madison to Wausau. The scale of this map is 1inch:13 miles. What is the actual distance between Madison and Wausau to the nearest mile?

8. Find the actual distance between City Hall and El Centro College.

9. Lady Liberty holds a tablet in her left hand. The tablet is 7
Lady Liberty holds a tablet in her left hand. The tablet is 7.19 m long and 4.14 m wide. If you made a scale drawing using the scale 1 cm:0.75 m, what would be the dimensions to the nearest tenth?

10. The rectangular central chamber of the Lincoln Memorial is 74 ft long and 60 ft wide. Make a scale drawing of the floor of the chamber using a scale of 1 in.:20 ft.

11. Explore dilations further
Record observations using a scale factor of 2.
Characteristics
Original Triangle ABC
New Triangle A’B’C’
Observations
Coordinates
A(3,5) B(3,2) C(7,2)
Angle Measures
53ᵒ - 90ᵒ - 37ᵒ
Length of Sides
Perimeter
Area

12. Explore dilations further
Record observations using a scale factor of 1/2.
Characteristics
Original Rectangle ABCD
New Rectangle A’B’C’D’
Observations
Coordinates
A(-2,4), B(-2,-2), C(4,-2), D (4,4)
Angle Measures
90ᵒ - 90ᵒ -90ᵒ - 90ᵒ
Length of Sides
Perimeter
Area

15. Given that ∆LMN:∆QRT, find the perimeter P and area A of ∆QRS.

16. ∆ABC ~ ∆DEF, BC = 4 mm, and EF = 12 mm
∆ABC ~ ∆DEF, BC = 4 mm, and EF = 12 mm. If P = 42 mm and A = 96 mm2 for ∆DEF, find the perimeter and area of ∆ABC.

17. m  AGF=108
GF=14, AD=12
DG = 4.5, EF = 8
AB = 26
1. What is the similarity ratio of ABCD to AEFG?
2. AG 3. DC
4. m  ADC 5. BC
6. Perimeter of ABCD and AEFG
7. Ratio of the Perimeters of ABCD to AEFG
8. Ratio of the Areas of ABCD to AEFG

18. Lesson Quiz: Part I
1. Maria is 4 ft 2 in. tall. To find the height of a flagpole, she measured her shadow and the pole’s shadow. What is the height h of the flagpole?
2. A blueprint for Latisha’s bedroom uses a scale of 1 in.:4 ft. Her bedroom on the blueprint is 3 in. long. How long is the actual room?

19. Lesson Quiz: Part II
3. ∆ABC ~ ∆DEF. Find the perimeter and area of ∆ABC.