GT Geom Drill 3.17

1. Take out HW and a pen and put it on the corner of your desk.

2. Objective:STW write and simplify ratios and use proportions to solve problems.

STW discover properties of similar polygons

GT Geometry Drill #3.17 2/28/14

Solve for X

x

x

8

5

2.3

3

4

2

3.1

23

10

2

1.4

3

2

14

12.2

xx

x

x

x

5. The ratio of the side lengths of a triangle is 4:7:5, and its perimeter is 96 cm. What is the length of the shortest side?

Let the side lengths be 4x, 7x, and 5x. Then 4x + 7x + 5x = 96 . After like terms are combined, 16x = 96. So x = 6. The length of the shortest side is 4x = 4(6) = 24 cm.

6. The ratio of the angle measures in a triangle is 1:6:13. What is the measure of each angle?

GT Geometry Drill #3.17 2/28/14

Holt McDougal Geometry

7-1 Ratio and Proportion

The ratio of the angle measures in a triangle is 1:6:13. What is the measure of each angle?

x + y + z = 180°

x + 6x + 13x = 180°

20x = 180°

x = 9°

y = 6x

y = 6(9°)

y = 54°

z = 13x

z = 13(9°)

z = 117°

Holt McDougal Geometry

7-1 Ratio and Proportion

? ? ?

Holt McDougal Geometry

7-1 Ratio and Proportion

21 12 2828

3 1524 20

6 8 38 4 15

16 15 52720 10

36 1214

Holt McDougal Geometry

7-1 Ratio and Proportion

Example 4: Using Properties of Proportions

Given that 18c = 24d, find the ratio of d to c in simplest form.

18c = 24d

Divide both sides by 24c.

Simplify.

Holt McDougal Geometry

7-1 Ratio and Proportion

Check It Out! Example 4

Given that 16s = 20t, find the ratio t:s in simplest form.

16s = 20t

Divide both sides by 20s.

Simplify.

Holt McDougal Geometry

7-1 Ratio and Proportion

Example 5: Problem-Solving Application

1 Understand the Problem

The answer will be the length of the room on the scale drawing.

Marta is making a scale drawing of her bedroom. Her rectangular room is 12 feet wide and 15 feet long. On the scale drawing, the width of her room is 5 inches. What is the length?

Holt McDougal Geometry

7-1 Ratio and Proportion

Example 5 Continued

2 Make a Plan

Let x be the length of the room on the scale drawing. Write a proportion that compares the ratios of the width to the length.

Holt McDougal Geometry

7-1 Ratio and Proportion

Solve3

Example 5 Continued

Cross Products Property

Simplify.

Divide both sides by 12.5.

5(15) = x(12.5)

75 = 12.5x

x = 6

The length of the room on the scale drawing is 6 inches.

Agree or Disagree1. If two figures are similar then they are congruent

2. If the ratios of the length of corresponding sides of two triangles are equal, then the triangles are congruent.

3. If triangles are similar then they have the same shape

4. If two triangles are congruent then each pair of corresponding angles are congruent.

5. If two angles of one triangle are congruent to corresponding angles of another triangle, then the triangles are similar

similarsimilar polygonssimilarity ratio

Vocabulary

Figures that are similar (~) have the same shape but not necessarily the same size.

Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding side lengths are proportional.

Proving Similar Triangles

•Are the triangles similar?

1512

18

16 20

24

Are these similar?

6

5

2181

5

6

Scale Factor

The ratio of the lengths of two corresponding sides of similar polygons.