Kickoff 7.5.1

Performance Based Objective: Students will be able to use ratios and scale drawings in order to make indirect measurements, solve problems and understand how perimeter and area are affected when a figure is resized.

Holt McDougal Geometry

7-5

Using Proportional Relationships

Kickoff 7.5.2

Today’s Goals: Use ratios to make indirect measurements. Use scale drawings to solve problems.

Holt McDougal Geometry

7-5

Using Proportional Relationships

Use ratios to make indirect measurements.

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Use scale drawings to solve problems.

Objectives

indirect measurement

scale drawing

scale

Vocabulary

Holt McDougal Geometry

7-5

Using Proportional Relationships

Indirect measurement is any method that uses formulas, similar figures, and/or proportions to measure an object. The following example shows one indirect measurement technique.

Holt McDougal Geometry

7-5

Using Proportional Relationships

Holt McDougal Geometry

7-5

Using Proportional Relationships

Holt McDougal Geometry

7-5

Using Proportional Relationships

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.

Holt McDougal Geometry

7-5

Using Proportional Relationships

Problem Solving 1. A triangular painting at the Louvre is 7 meters tall. The area of this painting is 49 meters² and its perimeter 42 meters. A scale drawing measures 3.2 cm tall. Make a drawing representing this scenario and use it to find the area and perimeter of the scale drawing.

Holt McDougal Geometry

7-5

Using Proportional Relationships

Problem Solving 2. The top of the flatiron building has an area that measures 289 ft². A scale drawing has an area that measures 169 mm². Suppose one side of the scale drawing measures 57 mm wide. What is the width of the actual flatiron building?

Holt McDougal Geometry

7-5

Using Proportional Relationships

Problem Solving 3. In the diagram below, ΔABC ∼ ΔDEC. If AC = 12, DC = 7, DE = 5, and the perimeter of ΔABC is 30, what is the perimeter of ΔDEC? Suppose the area of ΔABC = 144 units², what is the area of ΔDEC?

Holt McDougal Geometry

7-5

Using Proportional Relationships

Practice today’s concepts independently on Deltamath.com

7.5 Using Proportional Relationships

Holt McDougal Geometry

7-5

Using Proportional Relationships

Exit Ticket:

1. How is perimeter related to the similarity ratio?

2. How is area related to the similarity ratio?

3. When two polygons are similar what is true about their corresponding angles?

4. When two polygons are similar what is true about their corresponding sides?

Holt McDougal Geometry

7-5

Using Proportional Relationships

Example 1: Measurement Application

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?

Holt McDougal Geometry

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Using Proportional Relationships

Example 2: Solving for a Dimension

Holt McDougal Geometry

7-5

Using Proportional Relationships

Example 3: Making a Scale Drawing

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 of the scale drawing to the nearest tenth? What would the area be?

Holt McDougal Geometry

7-5

Using Proportional Relationships

Example 4: Using Ratios to Find Perimeters and Areas

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

Holt McDougal Geometry

7-5

Using Proportional Relationships

Kickoff 7.5.2

Performance Based Objective: Students will be able to use ratios and scale drawings in order to make indirect measurements, solve problems and understand how perimeter and area are affected when a figure is resized.

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Holt McDougal Geometry

7-5

Using Proportional Relationships

1. How is perimeter affected when a figure is resized?

2. How is the area affected when a figure is resized?

Holt McDougal Geometry

7-5

Using Proportional Relationships

Example 5: Using Ratios to Find Perimeter and Area

Triangle RJM has an area of 6 and a perimeter of 12. If the triangle is dilated by a scale factor of 3 centered at the origin, what are the area and perimeter of its image, triangle R’J’M’?

Holt McDougal Geometry

7-5

Using Proportional Relationships

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?

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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?

Holt McDougal Geometry

7-5

Using Proportional Relationships

Lesson Quiz: Part II

3. ∆ABC ~ ∆DEF. Find the perimeter and area of ∆ABC.

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Holt McDougal Geometry

7-5

Using Proportional Relationships

Objective: Assess and improve our knowledge of Geometry topics 6.1 - 7.5

Proceed to Google Classroom: Use the 6.1 - 7.5 Quiz Bubble Sheet to submit your answers to the exam. Mark your exam to check your answers.

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Work on corrections and then mastery.

Chap 6: need 11 correct on ques 1 - 13

Chap 7: need 9 correct on ques 14 - 24

Holt McDougal Geometry

7-5

Using Proportional Relationships

Kickoff 7.5 Exp. 1

3. Find the distance from

the front to the back of an

end zone

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4. Find the length of the field from the back of one end zone to the back of the other

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5. Estimate the width of the field to the nearest yard.

Today’s Goals: Use ratios to make indirect measurements. Use scale drawings to solve problems.

Holt McDougal Geometry

7-5

Using Proportional Relationships

Kickoff 7.5 Day 2

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

5. Suppose you are given a small rectangle, and a similar rectangle three times in size. How many small rectangles could fill the larger rectangle?

Today’s Goals: Use ratios to make indirect measurements. Use scale drawings to solve problems.

Holt McDougal Geometry

7-5

Using Proportional Relationships

Kickoff 7.5 Exp. 1

1. ABCD and EFGH are rectangles.

Explain why ABCD ~ EFGH.

2. Find the similarity ratio of ABCD to EFGH.

3.

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4. Ratio of the perimeters? Ratio of the areas?

5. How do the ratios in Step 4 compare to the similarity ratio?

7. Explain how to find the ratio of the perimeters of two polygons whose similarity ratio is a:b

8. Explain how to find the ratio of the areas of two polygons whose similarity ratio is a:b

Today’s Goals: Use ratios to make indirect measurements. Use scale drawings to solve problems.

Holt McDougal Geometry

7-5

Using Proportional Relationships