7.1 Ratio and Proportion Geometry Ms. Kelly Slide #1

Objectives 7.1 Ratio and Proportion 7.2 Properties of Proportions Express a _____ in simplest form. Solve for an unknown term in a given proportion. Slide #2

Real Life Applications Let’s list on the board where you find ratios and proportions in real life. (1st block) Slide #3

Real Life Applications Let’s list on the board where you find ratios and proportions in real life. (3rd block) Slide #4

Definitions Ratio What is looks like….. The ratio of one number to another is the _______ when the first number is ______ by the second. Its usually expressed in simplest form. The ratio of 8 to 12 is ______, or ______. If y ≠ 0, then the ration of x to y is _______. Slide #5

Ex. 1: Simplifying Ratios Simplify the ratios: 12 cm b. 6n2 c. 9p 4 cm 18n 18p Slide #6

Example 2 Find the ratio of OI to ZD Using the same trapezoid… Find the ratio of the measure of the smallest angle of the trapezoid to that of the largest angle. Slide #7

Ratios in Form a:b Sometimes the ratio of a to b is written in the form a:b. This form can also be used to compare three of more numbers, like a:b:c. Example: The measures of the three angles of a triangle are in the ratio 2:2:5. Find the measure of each angle. Slide #8

Ex. 3: Using Extended Ratios The measures of the angles in ∆JKL are in the extended ratio 1:2:3. Find the measures of the angles. Begin by sketching a triangle. Then use the extended ratio of 1:2:3 to label the measures of the angles as x°, 2x°, and 3x°. 2x° 3x° x° Slide #9

Solution: Statement x°+ 2x°+ 3x° = 180° 6x = 180 x = 30 Reason Triangle Sum Theorem Combine like terms Divide each side by 6 So, the angle measures are 30°, 2(30°) = 60°, and 3(30°) = 90°. Slide #10

More examples of a:b Find the ratio and express in simplest form. Slide #11

Proportion What it is… What is looks like…. A proportion is an equation stating that ____ ratios are equal. When three of more ratios are equal, you can write an extended proportion. Slide #12

Closure to 7.1 Ticket to stay in class Answers Three numbers aren’t known but the ratio of the numbers is 1:2:5. Is it possible that the numbers are: 10, 20 and 50? 3, 6, and 20? x, 2x, 5x Slide #13

Classwork Page 243 1-4, 8-11 on mini-white boards or whiteboards Slide #14

Properties of Proportions 7.2 Properties of Proportions Slide #15

Using Proportions An equation that equates two ratios is called a proportion. For instance, if the ratio of a/b is equal to the ratio c/d; then the following proportion can be written: Means Extremes  =  The numbers a and d are the extremes of the proportions. The numbers b and c are the means of the proportion. Slide #16

Properties of proportions CROSS PRODUCT PROPERTY. The product of the extremes equals the product of the means. If  = , then ad = bc Slide #17

Properties of proportions RECIPROCAL PROPERTY. If two ratios are equal, then their reciprocals are also equal. If  = , then =  b a To solve the proportion, you find the value of the variable. Slide #18

Ex. 4: Solving Proportions 5 Write the original proportion. Reciprocal prop. Multiply each side by 4 Simplify. = x 7 4 x 7 4 = 4 5 28 x = 5 Slide #19

Ex. 5: Solving Proportions 3 2 Write the original proportion. Cross Product prop. Distributive Property Subtract 2y from each side. = y + 2 y 3y = 2(y+2) 3y = 2y+4 y 4 = Slide #20

Example 6 - Factoring Slide #21

Example 7 In the figure, If CE = 2, EB = 6 and AD = 3, then DB = ___ If AB = 10, DB = 8, and CB = 7.5, then EB =___ Slide #22

Homework Page 243-244 1-14, 21-30 Page 247 – 248 9-29 odds, 33-38 Slide #23