Presentation on theme: "Special Ratios Similar Figures: Scale Factor Ratio of Perimeters"— Presentation transcript:
1 Special Ratios Similar Figures: Scale Factor Ratio of Perimeters Ratio of Areas
2 What is the scale factor for the similar parallelograms? Solve for x in the pair of similar triangles.168153025x1230
3 Special Ratios in Similar Figures 35610Scale Factor:Ratio of the perimeters= Scale FactorOROROR
4 12 : 22 15 : 60 1 : 4 b a Area Ratio Scale Factor 6 3 5 10 15 : 60Ratio of AreasSimplify1 : 4
5 Area Ratio is 32 : 52 9 : 25 Area Ratio Example Given the Scale Factor is 3 : 5Area Ratio is 32 : 529 : 25
6 Example 1 The two rectangles are similar. a. Find their scale factor. Use one pair of corresponding sides andsimplify the ratio.The scale factor is 2 : 3.b. Find the ratio of their perimeters.This is the same as the scale factor or 2 : 3c. Find the ratio of their areas.Square the scale factor or 4 : 9
7 Example 2The similar figures above have a scale factor 3 : 4. The smallerfigure has a perimeter of 15 inches. Find the perimeter of the largerfigure.Ratio of perimeters is the same as the scale factor : 4Write a proportion.Use cross products to solve x = 60x = 20The larger figure has a perimeter of 20 inches.
8 Example 3 The similar octagons above have a scale factor 2 : 5. a. Find the ratio of their areas.Square the scale factor : 52 → 4 : 25b. The larger figure has an area of 100 ft2. Find the areaof the smaller figure.Write a proportion.Use cross products to solve x = 400x = 16The smaller octagon has an area of 16 ft2.
9 Example 4ab Two similar paintings have perimeters of 20 in and 40 in. a. Find the scale factor.The scale factor is the same or 1 : 2as the ratio of perimeters.b. Find the ratio of the areas.Square the scale factor : 22 → 1 : 4
10 Example 4c Two similar paintings have perimeters of 20 in and 40 in. The ratio of their areas is 1: 4.c. The smaller area is 24 in2. Find the larger area.Write a proportion using the ratio of the areas.Use cross products to solve x = 96The larger area is 96 in2.
11 Exit Problems Use the similar hexagons below. Find their scale factor.Find the ratio of their perimeters.Find the ratio of their areas.Two similar triangles have perimeters of 12 m and 60 m1812
12 Communication PromptDylan has two similar trees in his backyard. One tree is twice as tall as the other. Suppose the trees were cut down in corresponding places. Each stump had a shape of a circle at its top. Is the area of the larger circle twice as big as the area of the smaller stump’s circle? Why or why not?
13 Special Ratios for Similar Figures Lesson 10ProportionalitySpecial Ratios for Similar Figures
16 Special Ratios for Similar Figures If two figures are similar and the ratio of their sidessimplifies to a :b, then:The scale factor is a :bThe ratio of the perimeters is a :bThe ratio of the areas is a2:b2