S IMILAR S HAPES AND P ROPORTIONS MATH 8 MS. STEWART Outcome: E3 make and apply generalizations about the properties of similar 2-D shapes.

Slides:



Advertisements
Similar presentations
I can use proportions to find missing measures in similar figures
Advertisements

Application of Proportions
Proportions This PowerPoint was made to teach primarily 8th grade students proportions. This was in response to a DLC request (No. 228).
2.5 Solving Proportions Write and use ratios, rates, and unit rates. Write and solve proportions.
Using Cross Products Lesson 6-4. Cross Products When you have a proportion (two equal ratios), then you have equivalent cross products. Find the cross.
Pre-Algebra 7-7 Scale Drawings Learn to make comparisons between and find dimensions of scale drawings and actual objects.
Similar Triangles and other Polygons
Find the slope of the line through each pair of points.
Ratio 11/12 My bike’s fuel has a ratio of oil to gas 1 : 25.
Similar Figures 4-3 Problem of the Day A rectangle that is 10 in. wide and 8 in. long is the same shape as one that is 8 in. wide and x in. long. What.
Applications Proportions
Similar Figures (Not exactly the same, but pretty close!)
By: Taylor M..  Two figures with the same shape and size.  over there, there’s two triangles exactly the same but moved to different places. 
Copyright © Cengage Learning. All rights reserved. Rational Expressions and Equations; Ratio and Proportion 6.
PRE-ALGEBRA. Lesson 6-3 Warm-Up PRE-ALGEBRA What are “similar figures”? similar figures: figures that have the same exact shape but not the same size.
Warm Up Find the slope of the line through each pair of points. 1. (1, 5) and (3, 9) 2. (–6, 4) and (6, –2) Solve each equation. 3. 4x + 5x + 6x = 45 4.
MATRIX GRANT PROJECT DIANA DIANA ROOM 606 ROOM 606 SCHOOL#14 SCHOOL#14.
Proportional Reasoning Today you will learn to: test if ratios can form a proportion. use cross products. M7.A.2.2.3: Use proportions to determine if two.
{ Section 8.1 Ratio and Proportion OBJECTIVE: To write ratios and solve proportions To write ratios and solve proportions BIG IDEA:Proportionality ESSENTIAL.
Proportions Mrs. Hilton’s Class. Proportions What are proportions? - If two ratios are equal, they form a proportion. Proportions can be used in geometry.
Target: Use proportions to solve problems involving similar figures.
Solve the following proportions. a = 9 b = 7 c = 6 d = 6.
Bell Work Find the measure of the missing value in the pair of similar polygons. (Shapes not drawn to scale.) 1. x 30 m 7 m 70 m 3 m 2. 2 mm x 5 mm 27.5.
Unit 7 Similarity. Part 1 Ratio / Proportion A ratio is a comparison of two quantities by division. – You can write a ratio of two numbers a and b, where.
Solving Proportions. 2 ways to solve proportions 1. Equivalent fractions (Old) Cross Products (New)
8-1 R ATIOS AND P ROPORTIONS M11.C D Objectives: 1) To write ratios and solve proportions.
Transparency 6 Click the mouse button or press the Space Bar to display the answers.
Pre-Algebra T McDowell
B ELL R INGER T HROW B ACK T HURSDAY Write each expression using exponents x 4 x 4 x 4 x 4 2. Y x Y x Y 3. (p)(p)(p) 4. (3w)(3w)(3w)(3w)
Proportions. State of the Classes Chapter 4 Test2 nd 9 week average
Solve the following proportions. a = 9 b = 7 c = 6 d = ±6.
P.O.D. Use your knowledge of proportions to solve for x = x 24 3  24 = 8  x 72 = 8x ÷8 9 = x Use your knowledge of proportions to solve for t.
2.8 – Proportions & Similar Figures “I can solve proportions using scale factors.” “I can find missing side lengths of similar figures.”
Cross Products and Proportions
 You can use similar figures to find missing information about one of the figures, when you know the measurements of at least one of the figures and.
  A ratio is a way to compare two quantities that are measured in the same units by using division  45 : 100 Ratio.
8 Date: Topic: Similar Triangles __ (7.5) Warm-up: 6 The shapes are similar. Find the similarity ratio, x, and y y 93° x x Similarity ratio =
Groundhog Day A 16 inch tall groundhog emerges on Groundhog Day near a tree and sees its shadow. The length of the groundhog’s shadow is 5 inches, and.
Unit 1 Test Part 2 First Name and Last Name Period Date Mr. Menjivar/Pre-Algebra StandardScore NS 1.2 NS 2.2.
Indirect Measurement. Indirect Measurement: Allows you to use properties of similar polygons to find distances or lengths that are difficult to measure.
Ratios, Proportions and Similar Figures
Solving proportions.
5-6 to 5-7 Using Similar Figures
Perimeters and Areas of Similar Figures
SIMILAR TEST REVIEW STUDY, STUDY, STUDY!!!.
Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.
Ratios, Proportions and Similar Figures
Similar Polygons & Scale Factor
Lesson 5-1 Using Proportions.
Lesson 6.1 How do you find ratios and unit rates?
Ratios and Proportions
Using Proportions.
Ratios, Proportions and Similar Figures
Ratios, Proportions and Similar Figures
Chapter 10 Similarity.
Rates, Ratios and Proportions
7-7 Scale Drawings Warm Up Problem of the Day Lesson Presentation
Proportions This PowerPoint was made to teach primarily 8th grade students proportions. This was in response to a DLC request (No. 228).
Section 8.1 Ratio and Proportion
Ratios, Proportions and Similar Figures
Similar Figures The Big and Small of it.
Ratios, Proportions and Similarity
PROPORTIONS.
7.1 Ratio and Proportion.
Similar Polygons & Scale Factor
Ratios, Proportions and Similar Figures
Using Cross Products Chapter 3.
Rates, Ratios and Proportions
Proportions This PowerPoint was made to teach primarily 8th grade students proportions. This was in response to a DLC request (No. 228).
Similar figures & scale drawings
Presentation transcript:

S IMILAR S HAPES AND P ROPORTIONS MATH 8 MS. STEWART Outcome: E3 make and apply generalizations about the properties of similar 2-D shapes

H OW ABOUT A CLIP TO GET US STARTED ?

P ROPORTIONS What are proportions? - If two ratios are equal, they form a proportion. Proportions can be used in geometry when working with similar figures. What do we mean by similar? - Similar describes things which have the same shape but are not the same size = 1:3 = 3:9

E XAMPLES These two stick figures are similar. As you can see both are the same shape. However, the bigger stick figure’s dimensions are exactly twice the smaller. So the ratio of the smaller figure to the larger figure is 1:2 (said “one to two”). This can also be written as a fraction of ½. A proportion can be made relating the height and the width of the smaller figure to the larger figure: 2 feet 4 feet 8 feet 4 feet 4 2 = 8 4

S OLVING P ROPORTIONAL P ROBLEMS So how do we use proportions and similar figures? Using the previous example we can show how to solve for an unknown dimension. 2 feet 4 feet 8 feet ? feet

S OLVING P ROPORTION P ROBLEMS First, designate the unknown side as x. Then, set up an equation using proportions. What does the numerator represent? What does the denominator represent? Then solve for x by cross multiplying: 2 feet 4 feet 8 feet ? feet 4 2 = 8 x 4x = 16 X = 4

T RY O NE Y OURSELF Knowing these two stick figures are similar to each other, what is the ratio between the smaller figure to the larger figure? Set up a proportion. What is the width of the larger stick figure? 4 feet 8 feet 12 feet x feet

S IMILAR S HAPES In geometry similar shapes are very important. This is because if we know the dimensions of one shape and one of the dimensions of another shape similar to it, we can figure out the unknown dimensions.

P ROPORTIONS AND T RIANGLES What are the unknown values on these triangles? 16 m 20 m 4 m 3 m x y First, write proportions relating the two triangles = 3 x 4 = y 20 Solve for the unknown by cross multiplying. 4x = 48 x = 12 16y = 80 y = 5

T RIANGLES IN THE R EAL W ORLD Do you know how tall your school building is? There is an easy way to find out using right triangles. To do this create two similar triangles using the building, its shadow, a smaller object with a known height (like a yardstick), and its shadow. The two shadows can be measured, and you know the height of the yard stick. So you can set up similar triangles and solve for the height of the building.

S OLVING FOR THE B UILDING ’ S H EIGHT Here is a sample calculation for the height of a building: 48 feet 4 feet 3 feet yardstick building x x 3 = x = 144 x = 36 The height of the building is 36 feet.