Similarity M7G3.a Understand the meaning of similarity, visually compare geometric figures similarity, and describe similarities by listing corresponding.

Slides:



Advertisements
Similar presentations
Introduction Recognizing and using congruent and similar shapes can make calculations and design work easier. For instance, in the design at the corner,
Advertisements

Section 8.3 Similar Polygons
56.) Congruent Figures—figures that have the same size and shape 57.) Similar Figures—figures that have the same exact shape but different size (angles.
Proportions  A proportion is an equation with a ratio on each side. It is a statement that two ratios are equal.  3 = 6 is an example of a proportion.
5-5 Similar Figures Warm Up Problem of the Day Lesson Presentation
Using Proportions to Solve Geometry Problems Section 6.3.
6.3 Use Similar Polygons. Objectives IIIIdentify similar polygons SSSSolve problems using proportions with similar polygons.
Similar Figures Similar Figures Definition of Similar Figures Similar figures are figures that have the same shape but not necessarily the same size. Example:
Ratios, Proportions, and Similar Triangles. Ratios Ratios are like fractions The ratio 1:4 means 1 part to 4 parts and is equivalent to the fraction (part:part)
Proportions & Similar Figures
A Quadratic Equation is an equation that can be written in the form Solving Quadratic Equations – Factoring Method Solving quadratic equations by the factoring.
Geometry Warm-Up1/13/11 1) In a triangle, the ratio of the measures of three sides is 3:4:5, and the perimeter is 42 feet. Find the measure of the longest.
Solve the following proportions. a = 9 b = 7 c = 6 d = 6.
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.
7-2 Similar Polygons Objective To identify and apply similar polygons.
1 Objectives To set up ratios and solve proportions To identify similar polygons using ratios.
Geometry 6.3 Big Idea: Use Similar Polygons
Solve the following proportions. a = 9 b = 7 c = 6 d = ±6.
Course Similar Figures Warm Up Solve each proportion. b = y5y5 = p9p9 = m = 4. b = 10y = 8 p = 3 m = 52.
8.3 Similar Polygons Geometry.
8.3 Similar Polygons. Identifying Similar Polygons.
Transparency 5 Click the mouse button or press the Space Bar to display the answers.
7-1B Similar Polygons What is a proportion? What are proportions used for in Geometry? What Geometry symbol is used for “is similar to”? What similar figure.
Warm up… Reflect on the first six weeks. What will you as an individual do differently this six weeks to achieve the grade you want in this class? Whether.
7.2—Similar Polygons. Identifying Similar Polygons When there is a correspondence between two polygons such that their corresponding angles are congruent.
Similar Triangles Triangles that have the same shape but not necessarily the same size. Corresponding angles are congruent. Meaning they have the same.
Warm-Up If ∆QRS  ∆ZYX, identify all 3 pairs of congruent angles and all 3 pairs of congruent sides.
8.3 Similar Polygons. Identifying Similar Polygons.
Unit 1 Transformations Day 5.  Similar Polygons - Two figures that have the same shape but not necessarily the same size ◦ Symbol: ~ ◦ Similar Polygons.
Ratio and Proportion Day 8. Day 8 Math Review Math Review Quiz Day.
7.2 Similar Polygons. Objectives  Identify similar polygons  Use similar polygons to solve real-life problems, such as making an enlargement similar.
 Two polygons are similar polygons if corresponding angles are congruent and if the lengths of corresponding sides are proportional.
A ratio is a quotient of two numbers. The ratio of two numbers, a & b can be written as a to b, a:b, or a/b, (where b = 0). Examples: to 21:21/2.
By: Katerina Palacios similar polygons: When 2 polygons are similar that means that they have the same looking shape but they do not have the.
Lesson Menu Main Idea and New Vocabulary NGSSS Key Concept:Similar Polygons Example 1:Identify Similar Polygons Example 2:Find Missing Measures Key Concept:Ratios.
6.3.1 Use similar Polygons Chapter 6: Similarity.
Geometry 7.2 SWLT: Use Proportions to identify similar polygons.
6.2 Similar Polygons What you’ll learn: To identify similar figures.
Warm-up Proportions WS Can you solve for x AND Y? 2 = X = Y.
Geometry 6.3 SWLT: Use Proportions to identify similar polygons.
Unit 8.3 Similar Polygons.
Objective To identify and apply similar polygons
2-1: Properties of Similar Polygons
Bell Work: Solve the proportion 9 = 18 3 d
G-11 Similar Triangles I can demonstrate the equality of corresponding angles and proportionality of sides using similarity and similarity transformations.
8.3 Similar Polygons Geometry.
Similar Polygons.
7-2 Similar Polygons.
Similar Figures.
Objectives: To identify similar polygons To apply similar polygons
6.3 Use Similar Polygons.
Similar Polygons.
Chapter 2 Similarity and Dilations
Test study Guide/Breakdown
8.4 Similar Polygons Sec Math 2.
Main Idea and New Vocabulary Key Concept: Similar Polygons
Lesson 6.1 How do you find ratios and unit rates?
8.3 Similar Polygons.
8.3 Similar Polygons Geometry Mr. Qayumi 2010.
Objectives Identify similar polygons.
Warm Up The geometric mean of 12 and another number is 30. What is the other number?
8.4 Similar Polygons Sec Math 2.
Lesson 13.1 Similar Figures pp
Drill Find x, if the semicircle arc of a circle is 3x + 30 degrees.
8.3 Similar Polygons.
LEARNING GOALS – LESSON 7:2
Chapter 8 Similarity.
Chapter 8 Similarity.
Warm Up Find the slope of the line through each pair of points.
Chapter 8 Similarity.
Presentation transcript:

Similarity M7G3.a Understand the meaning of similarity, visually compare geometric figures similarity, and describe similarities by listing corresponding parts.

What is Similarity? Not Similar Similar Not Similar

Ratios A ratio is a way to compare two numbers. The ratio of x to y can be written in three ways: x to y, x:y, x/y Ratios are expressed in simplified form: The ratio of 6:8 is simplified to 3:4 Ratios that have different units of measure, must be converted to like units before they are simplified.

A C B F ED 3 inches 8 inches The ratios of the sides lengths of  DEF to the corresponding sides lengths of  ABC are 2:1. Find the unknown lengths DF=AB= Similar Figures

Similar Polygons Similarity between two polygons: symbol is ~ Corresponding angles are equal (marked with arcs) Lengths of the sides of the polygon are proportional

List all of the pairs of the equal (congruent  ) angles.

Similar Polygons What is the measure of angle b?

List the ratio of side lengths: is called the scale factor

What is the scale factor? Since these two polynomials are similar, calculate the scale factor W X Y B P QR S

Proportions A proportion is an equation stating that two ratios (written as fractions) are equal. You can check to see if two ratios form a proportion using their cross product. Since we know that cross products work for proportions, we can use them to solve for a variable. x = 6

Example using a proportion M K L J SR QP x Quadrilateral JKLM is similar to quadrilateral PQRS. Find the value of x. x = 4

x Real Life Application: Photographic Enlargements You have been asked to create a poster to advertise a CD for Chris Brown You have a 4 inch by 5 inch photo for you to enlarge. You want the enlargement to be 16 inches wide. How long will it be? 4 16