Similar Triangles and Polygons

Slides:

Advertisements

Similar presentations

10-4 Perimeters and Areas of Similar Figures

Advertisements

EXAMPLE 3 Use a ratio of areas Cooking SOLUTION First draw a diagram to represent the problem. Label dimensions and areas. Then use Theorem If the.

EXAMPLE 2 Use a ratio to find a dimension SOLUTION Painting You are planning to paint a mural on a rectangular wall. You know that the perimeter of the.

EXAMPLE 3 Use a ratio of areas Then use Theorem If the area ratio is a 2 : b 2, then the length ratio is a:b. Cooking A large rectangular baking.

Hosted by: Mrs. Owens and Miss Hiben. A Polygons B Perimeter C Area.

Applications of Geometry Example 1: The perimeter of a rectangular play area is 336 feet. The length is 12 feet more than the width. Determine the dimensions.

Section 8-6 Perimeter and Area of Similar Figures SPI 22d: determine the perimeter & area given the ratio of 2 similar polygons.

11.3 Perimeter and Area of Similar Figures. Two rectangles are similar. One has width 4 in. and length 6 in. The other has width of 6 in. and length of.

Determining Scale Factor We are learning to…use proportional reasoning to solve for missing side lengths of polygons. Wednesday, August 19, 2015.

A cube has a total surface area of 24 cm2

Scale Factor and Dilation

9-5 Warm Up Lesson Presentation Lesson Quiz Effects of Changing

10-5 Effects of Changing Dimensions Proportionally

Example 1: Effects of Changing One Dimension

11.3 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Perimeter and Area of Similar Figures.

Chapter Review Understand how to use formulas to find area and perimeter DO NOW: A particular rectangle has an area of 36 square feet and a.

8.6:Perimeters and Areas of Similar Figures

Perimeter & Area Lessons 19 & 20.

Geometry: Changing Dimensions

This is Math Jeopardy! Proportions Similar Polygons Similar Triangles Ratios Word Problems Miscellaneous

Changing Dimensions What’s the effect on Perimeter and Area??

1.3 Using Formulas Geometry Perimeter Measures the distance around the edge of any flat object. To find the perimeter of any figure, ADD the lengths.

Basic Measurement.

Scale Factor and the relationship to area and volume GLE SPI:

5 Minute Check Find the area. Complete on the back of

EXAMPLE 2 Use a ratio to find a dimension SOLUTION Painting You are planning to paint a mural on a rectangular wall. You know that the perimeter of the.

Effects of Changing Dimensions Proportionally 9-5 Holt Geometry.

9-5 Warm Up Lesson Presentation Lesson Quiz Effects of Changing

EXAMPLE 1 Finding Area and Perimeter of a Triangle Find the area and perimeter of the triangle. A = bh 1 2 P = a + b + c = (14) (12) 1 2 =

Course Similar Figures Warm Up Solve each proportion. b = y5y5 = p9p9 = m = 4. b = 10y = 8 p = 3 m = 52.

11.3 Perimeter and Area of Similar Figures Hubarth Geometry.

Lesson 8.4 Area of Triangles Pages How do you find the area of a triangle? Draw a triangle on the grid paper. Enclose the triangle in a rectangle.

The length of a rectangle is twice the width. The perimeter is 72 inches. Find the length and the width of the rectangle.

THINK LINE Imagine a line wrapped around the figure. Units are cm. ft. in. etc. 2 2 Perimeter is ONE DIMENSION DIMENSIONAL What is the Perimeter of.

10.4 Perimeters & Areas of Similar Figures

Perimeter, Circumference and Area. Perimeter and Circumference Perimeter : The distance around a geometric figure. Circumference: The distance around.

Warm Up Find the area of each figure. Give exact answers, using  if necessary. 1. a square in which s = 4 m 2. a circle in which r = 2 ft 3. ABC with.

7-1C Areas and Perimeters of Similar Polygons What is the relationship between the perimeter ratios of similar figures and their similarity ratio? What.

10.4 Perimeters and Areas of Similar Figures. Perimeters and Areas of Similar Figures  If the similarity ratio is, then:  The ratio of the perimeters.

Unit 8 – 6 Dimensional changes

Holt Geometry Warm Up Find the area of each figure. Give exact answers, using  if necessary. 1. a square in which s = 4 m 2. a circle in which r = 2 ft.

Warm Up Find the area of each figure. Give exact answers, using  if necessary. 1. a square in which s = 4 m 2. a circle in which r = 2 ft 3. ABC with.

PERIMETERS What is the Perimeter of a shape. What is the Perimeter of this rectangle? What is the Perimeter of this rectangle? 5cm 15cm.

8th Grade Math Unit 8 Review

C 5 4 A B 6 Z 10 8 X Y 12.

3rd Grade Math Module 7 Lesson 14

Model the polynomial with algebra tiles

Perimeters and Areas of Similar Figures

Objective: To find the perimeters and areas of similar figures.

LI: to calculate the perimeter of regular polygons.

11.3 – Perimeter and Area of Similar Figures

MEASUREMENT Given perimeter – find side length

Obj: to use ratios to solve problems

Warm Up Problem Which of the following expressions is equivalent to 6x + 24? A) 3(x + 12) B) 6(x – 4) C) 6(x + 4) D) x(6 + 4)

QUIZ REVIEW Interior Angle Measures

Objective - To identify how perimeter and area relate.

EXAMPLE 3 Use a ratio of areas Cooking

Use the substitution method to find all solutions of the system of equations {image} Choose the answer from the following: (10, 2) (2, 10) (5, - 2) ( -

Ratios, Rates and Percents

Warm Up Problem Find the area of the trapezoid..

Constructing Equations

Objectives Describe the effect on perimeter and area when one or more dimensions of a figure are changed. Apply the relationship between perimeter and.

Page 6 Original Expression: Step 1: Step 2: Step 3:

9-5 Warm Up Lesson Presentation Lesson Quiz Effects of Changing

Warm Up Find the area of each figure. Give exact answers, using  if necessary. 1. a square in which s = 4 m 2. a circle in which r = 2 ft 3. What’s bigger:

7.2 Ratios and proportions

Scale Factor and the relationship to area and volume

Volume of Prisms, Cross Sections and Scale Factors

Quiz, Perimeter and Area

11.7 Perimeters and Areas of Similar Figures

Presentation transcript:

Similar Triangles and Polygons

Is there a pattern? 4 cm 8 cm 16 cm 3 cm 6 cm Area: 12 cm2 12 cm

Is there a pattern? 5 in 10 in 20 in 6 in 12 in Area: 15 in2 24 in

Practice: If we double the length of the sides of this rectangle, what would be the new dimensions? What would the area of the new rectangle be? 12 m 8 m Area: 96 m2

What would the area of the new rectangle be? Practice: If we double the length of the sides of this rectangle, what would be the new dimensions? What would the area of the new rectangle be? 10 m 9 m Area: 90 m2

Is there a pattern? 7 cm 14 cm 28 cm 5 cm 10 cm Perimeter: 24 cm 20 cm

Is there a pattern? 4 in 2 in 8 in 4 in 16 in 8 in 3 in 6 in Perimeter: 9 in 12 in Perimeter: 18 in Perimeter: 36 in

What would the perimeter of the new rectangle be? Practice: If we double the length of the sides of this rectangle, what would be the new dimensions? What would the perimeter of the new rectangle be? 11 m 3 m Area: 27 m

What would the perimeter of the new triangle be? Practice: If we double the length of the sides of this triangle, what would be the new dimensions? What would the perimeter of the new triangle be? 15 cm 9 cm 12 cm Area: 36 cm

Application: What would happen to the perimeter of a similar triangle if the length of the sides were tripled? Justify by drawing a picture and showing the math.

Application: If the length and width of a rectangle are multiplied by 5, how does the area change? Justify by drawing a picture and showing the math.

Application: Use the following rectangle to answer these questions: What is the perimeter of the rectangle? What is the area of the rectangle? If the length and width of the rectangle are tripled, how will the perimeter change? 5 inches 3 inches

Challenge Question: A rug company has two sizes of rugs for sale. The length and width of the larger rug are twice the dimensions of the smaller one. The area of the larger rug is 96 ft2. What is the area of the smaller rug?

What size is the similar polygon? These two rectangles are similar and the ratio of their dimensions is 1:3. If the dimensions of the small rectangle are given, what are the dimensions of the large rectangle? 2 feet 4 feet

What size is the similar polygon? These two pentagons are similar and the ratio of their dimensions is 4:1. If the dimensions of the large pentagon are given, what are the dimensions of the small rectangle? 8 m 8 m 12 m 12 m 16 m

Application: A paper company has two sizes of poster board for sale. The dimensions of the smaller poster have a 1:2 to the large. If the smaller poster is 48 inches wide and 36 inches long, what are the dimensions of the larger poster board?

Challenge Question: Two similar triangles have a ratio of 1:2. If the dimensions of the small triangle are 10 ft, 10 ft, and 20 ft. What is the perimeter of the large triangle?

Challenge Question: Two similar triangles have a ratio of 5:1. If the dimensions of the large triangle are 50 ft, 50 ft, and 30 ft. What is the perimeter of the small triangle?