Introduction to Ratio, Proportion, and Similarity.

Slides:

Advertisements

Similar presentations

Ratios, Proportions, AND Similar Figures

Advertisements

Concept: Use Similar Polygons

Similar and Congruent Figures. Similar figures have the same shape, but not the same size. They must have the same ratio of side lengths Congruent figures.

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

7-4A Similar Figures and Proportions Learning Objective: To determine whether two given figures are similar, and to use similarity to find missing lengths.

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.

Using Proportions to Solve Geometry Problems Section 6.3.

8.1, 2, 7: Ratios, Proportions and Dilations

Lesson: 9 – 3 Similar Triangles

An in Depth Look at Ratios and Proportions and Their Applications.

7.1 and 7.2 Ratios and Proportions

7-1 Ratio and Proportion Warm Up Lesson Presentation Lesson Quiz

Chapter 6.1: Similarity Ratios, Proportions, and the Geometric Mean.

3-6 Ratios and Proportions Objective: Students will determine whether two ratios are proportional and solve proportions. S. Calahan 2008.

1 ratios 9C5 - 9C6 tell how one number is related to another. may be written as A:B, or A/B, or A to B. compare quantities of the same units of measurement.

Copyright © Cengage Learning. All rights reserved. Rational Expressions and Equations; Ratio and Proportion 6.

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)

Recognize congruent and similar figures. Find the scale factor of similar figures. Similar & Congruent Figures.

Solve the following proportions. a = 9 b = 7 c = 6 d = 6.

Geometry 6-1 Big Idea: Use Ratios & Proportions. A comparison of two numbers Ratio A comparison of two numbers Ex.1) ½, 1:2 Ex.2) 3, 3:4 4.

Course: Geometry pre-IB Quarter: 2nd

Chapter 7 Vocab Review. 1. Write the generic formula (proportion) for geometric mean (x) of two positive numbers a & b.

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.

A ratio is a comparison of two quantities using division. The ratio of quantities a and b can be expressed as a to b, a : b, or, where b ≠ 0. Ratios are.

WARM-UP 1.What triangle structures do Similarity and Congruence have in common? 2.Which structures are used only for Congruence? 3.Which structures are.

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.

Write and simplify ratios. Use proportions to solve problems. Objectives.

Math Pacing Ratios and Proportions Solve each equation

Triangle Similarity: Angle Angle. Recall Recall the definitions of the following: Similar Congruent Also recall the properties of similarity we discussed.

7-2 Similar Polygons Objectives Students will be able to:

Warm-Up If ∆QRS  ∆ZYX, identify all 3 pairs of congruent angles and all 3 pairs of congruent sides.

Unit 1 Transformations Day 5.  Similar Polygons - Two figures that have the same shape but not necessarily the same size ◦ Symbol: ~ ◦ Similar Polygons.

Date: Topic: Proving Triangles Similar (7.6) Warm-up: Find the similarity ratio, x, and y. The triangles are similar. 6 7 The similarity ratio is: Find.

Proportions & Similarity Advanced Geometry Similarity Lesson 2.

Ratio and Proportion Day 8. Day 8 Math Review Math Review Quiz Day.

 Two polygons are similar polygons if corresponding angles are congruent and if the lengths of corresponding sides are proportional.

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 =

TODAY IN GEOMETRY…  WARM UP: SRF and Rationalizing the Denominator  Learning Target: 6.3 Use properties of similar polygons to solve proportions.  Independent.

6.3.1 Use similar Polygons Chapter 6: Similarity.

Holt Geometry 7-1 Ratio and Proportion 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.

An in Depth Look at Ratios and Proportions and Their Applications.

CHAPTER 7.1 RATIO AND PROPORTION. RATIO A ratio compares two numbers by division. The ratio of two numbers a and b can be written as a to b; a:b; or a/b,

Congruent and Similar Figures

7.1 Proportions Solving proportions

Similarity in Triangles

Date: Topic: Similar Polygons (7.4)

Ratios, Proportions, and the Geometric Mean

6.3 Use Similar Polygons.

Using Proportions To Solve For Missing Sides

Warm Up(On a Separate Sheet)

Similar figures are figures that have the same shape but not necessarily the same size. The symbol ~ means “is similar to.” 1.

LEARNING GOALS – LESSON 7:1 EXAMPLE 1A: WRITING RATIOS

8.1 Exploring Ratio and Proportion

7-3 Similar Triangles.

Vocabulary 8.1 ratio proportion cross products similar

Lesson 6.1 How do you find ratios and unit rates?

SIMILAR POLYGONS Two figures are similar if

Vocabulary 8.1 ratio proportion cross products similar

Proving Triangles Similar.

Rates, Ratios and Proportions

Similar Triangles Panašūs trikampiai.

Proving Triangles Similar.

Ratios, Proportions and Similarity

7.1 Ratio and Proportion.

Warm Up Find the slope of the line through each pair of points.

Rates, Ratios and Proportions

Unit 4: Similarity Honors Geometry.

Congruent and Similar Triangles

Presentation transcript:

Introduction to Ratio, Proportion, and Similarity

Overview for the topic: - learn how to write and simplify ratios - learn how to determine whether two ratios are a proportion and how to use proportions to solve problems learn how to determine whether two triangles are similar

Ratio? What is a Ratio? A ratio is the comparison of two numbers using division. The ratio of x to y can be written or x:y. Ratios are usually expressed in simplest form.

Proportion? What is a Proportion? Since 2/4 and 3/6 are both equal to 1/2, they are equal to each other. A statement that two ratios are equal is called a proportion. A proportion can be written in one of the following ways: 2/4 =3/6or2:4 = 3:6

The first and last numbers in a proportion are called the extremes. The middle numbers are called the means. ProportionProportion

ProportionProportion In a proportion, the product of the means equals the product of the extremes. Means-Extremes Property

Triangle Similarity Two figures are similar if you can show that the following two statements are true: 1. Corresponding angles are congruent. 2. Corresponding sides are in proportion. 1. Corresponding angles are congruent. 2. Corresponding sides are in proportion.

Examples:

SOURCE:SOURCE: proportion-similarity/