6.1 Ratios, Proportions, and the Geometric Mean

Slides:



Advertisements
Similar presentations
7.1 Ratio and Proportion Geometry Ms. Kelly Slide #1.
Advertisements

CN #3 Ratio and Proportion
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.
Find the slope of the line through each pair of points.
6.1 – Ratios, Proportions, and the Geometric Mean Geometry Ms. Rinaldi.
6.1 – Ratios, Proportions, and the Geometric Mean
Bellwork – 1/6/15. Unit 6: Section 6.1 Ratios, Proportions, and the Geometric Mean (Starts on Page 356)
Ratio and Proportion.
7.1 Ratio and Proportion Textbook page 357.
7-1 Ratio and Proportion Warm Up Lesson Presentation Lesson Quiz
Objectives Write and simplify ratios.
Chapter 6.1: Similarity Ratios, Proportions, and the Geometric Mean.
Ratios and Proportions. Warm Up - Simplify Ratio – comparison of two numbers by division. Proportion – an equation stating that two ratios are equal.
Homework: Chapter 10-1 Page 499 # 1-27 Odds (Must Show Work)
7-1 Ratio and Proportion Warm Up Lesson Presentation Lesson Quiz
1/29/13. 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 x + 5 x + 6 x =
Warm Up Lesson Presentation Lesson Quiz
Geometry Section 6.1 Ratios, Proportions, and the Geometric Mean.
8.1: Ratios and Proportions
Warm-Up Solve each equation for x. 1) 3x = 5 2) 2x – 1 = 10 3) 5x + 3x = 14.
7-1 Using Proportions Recognize and use ratios and proportions.Recognize and use ratios and proportions. Apply the properties of proportions.Apply the.
Ratio and Proportion 7-1.
Chapter 6.1 Notes: Ratios, Proportions, and the Geometric Mean Goal: You will solve problems by writing and solving proportions.
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.
6.1.1 RATIOS, PROPORTIONS, AND THE GEOMETRIC MEAN Chapter 6: Similarity.
6.1 – Ratios, Proportions, and the Geometric Mean.
Course: Geometry pre-IB Quarter: 2nd
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.
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.
Chapter 6 Similarity Pre-Requisite Skills Page 354 all.
7-1 Ratios and Proportions I CAN Write a ratio Write a ratio expressing the slope of a line. Solve a linear proportion Solve a quadratic proportion Use.
 Students will be able to write and solve ratios  Students will be able to write and solve proportions.
Math Pacing Ratios and Proportions Solve each equation
8.1 Ratio and Proportion Geometry Ms. Reser.
Lesson 6-1 Proportions. Objectives Write ratios Use properties of proportions.
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.
Ratios and Proportions Section 7.1 Objective  Use ratios and proportions.
Holt Geometry 7-1 Ratio and Proportion 7-1 Ratio and Proportion Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson.
6.1 Ratios, Proportions and Geometric Mean. Objectives WWWWrite ratios UUUUse properties of proportions FFFFind the geometric mean between.
Ratios and Proportions
Entry task…. 1) The table below gives the wins and losses of a baseball team. In which year did the team have the best record? Explain. YearWinsLoses
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,
Find the slope of the line through each pair of points.
PROPORTIONS Write ratios Use properties of proportions
A ratio compares two numbers by division
Copyright © 2014 Pearson Education, Inc.
Ratios, Proportions, & Geometric Mean
Ratios, Proportions, and the Geometric Mean
7.1 Ratio and Proportions Pg 356
Before: March 28, 2016 An artist sketches a person. She is careful to draw the different parts of the person’s body in proportion. What does proportion.
Ratios and Proportions
Warm Up(On a Separate Sheet)
Lesson 5-1: Using Proportions
8.1 Ratio and Proportion.
Ratio and Proportion Unit IIA Day and 8.2.
Ratio & Proportions Practice
Chapter 7-1: Proportions
LEARNING GOALS – LESSON 7:1 EXAMPLE 1A: WRITING RATIOS
8.1 Ratio and Proportion.
8.1 Exploring Ratio and Proportion
7-1 Ratios and Proportions
Ratio Ratio – a comparison of numbers A ratio can be written 3 ways:
Ratios, Proportions, and the Geometric Mean
Lesson 5-1 Using Proportions.
You solved problems by writing and solving equations.
Lesson 5-1: Using Proportions
Ratios, Proportions, and the Geometric Mean
6.1 Ratios, Proportions, and the Geometric Mean
Warm Up Find the slope of the line through each pair of points.
Ratio A ratio is a comparison of two numbers such as a : b. Ratio:
Presentation transcript:

6.1 Ratios, Proportions, and the Geometric Mean Before: You solved problems by writing and solving equations Now: You will solve problems by writing and solving proportions Why?: Estimate populations, Doubling cookie recipes, creating blueprints

RATIO Ratio – a comparison of two numbers by division Can be written as: x to y x : y

RATIOS Ratios should be written in simplest form Can compare 3 numbers 4 to 2, or 4:2 must be reduced to 2:1 Is 3:18 in simplest form? Can compare 3 numbers 3 sides of a triangle a:b:c Units must be the same

EXAMPLE Left handed: Right Handed Right Handed: Left Handed Have a pet: Don’t have a pet

EXAMPLES In the 2002 Major League baseball season, Sammy Sosa hit 49 home runs and was at bat 556 times. Find the ratio of home runs to the number of times he was at bat. There are 182 girls in the sophomore class of 305. Find the ratio of girls to total students. The length of a rectangle is 8 in and its width is 5 in. Find the ratio of length to width.

Simplify Ratios Examples - Simplify the ratio 1 ft: 3 yards 1 yard=3 ft 3 L: 10 mL 1000 mL=1 L 3 in: 4 ft 12 in=1 ft 24 yards : 3 yards 60 mL : 6 L 15 in : 2 ft

Compare ratios of angles in a triangle The measures in the triangle are in the extended ratio of 1:2:3. Find the measure of the angles. Step 1:Sketch the triangle and label the angles with the extended ratio. x+2x+3x=180 Triangle Sum Theorem 6x=180 Combine like terms x=30 Divide each side by 6 Angle Measures are 30, 60, and 90

Your turn The measures in the triangle are in the extended ratio of 2:4:2. Find the measure of the angles.

Proportion – An equation stating that two ratios are equal PROPORTIONS Proportion – An equation stating that two ratios are equal What are the extremes and means of the following ratio?

Investigating Geometry Activity 6.1 Work in partnerships Notify me if your partner is not working and therefore should not receive credit Answer all questions!

Cross Products

PROPORTIONS How do you prove two ratios equal a proportion? Cross – Products! Do the following ratios form a proportion?

Do the following ratios form a proportion? PROPORTIONS Do the following ratios form a proportion? Check

What if one of the numbers is missing? PROPORTIONS What if one of the numbers is missing?

Geometric Mean Geometric Mean: If given two positive numbers (a and b) it is the x in the equation below.

Geometric mean Find the geometric mean of the two numbers 12 and 27

Your turn Find the geometric mean of the two numbers. 4 and 25

HOMEWORK Pg 360 #3-4, 7-8, 11-17 odd, 20-21, 23-35 odd