1 / 16

7.1 Ratio and Proportion

Geometry. 7.1 Ratio and Proportion. Ratio. The ratio of one number to another is the quotient when the first number is divided by the second. Simplest Form: ratio of 8 to 12 is If y ≠ 0, the ratio of x to y is. Ways to write a ratio. As a fraction. b ≠ 0. 2. With a colon a:b.

vera-manning
Download Presentation

7.1 Ratio and Proportion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Geometry 7.1Ratio and Proportion

  2. Ratio The ratio of one number to another is the quotient when the first number is divided by the second. Simplest Form: ratio of 8 to 12 is If y ≠ 0, the ratio of x to y is

  3. Ways to write a ratio • As a fraction b ≠ 0 2. With a colon a:b 3. With words a to b With ratios, unitsmust be the same.

  4. Ratios are used to compare two numbers, such as side length or angle measure, but the quantities being compared must be in the same units. Example: A sheet of plywood is 0.5m long by 35 cm wide. Find the ratio of the length to width. Notice that the units do not affect the final ratio. The ratio is the same no matter what measuring unit you use. Also, a ratio has no units attached to it. We can use ratio to find the measure of angles.

  5. Example: Two complementary angles have measures in the ratio 2:7. Find the measure of each angle.

  6. Ratios can compare more than two numbers. The notation used is a:b:c… Example: The measure of the five angles of a pentagon are in the ratio 11:7:5:4:3. Find the measure of each angle.

  7. Proportion: an equation that states that two ratios are equal. Examples: a:b = c:d 3:6 = 1:2 An extended proportion is an equation relating three or more ratios. Examples: x = ______ y = ________

  8. Express the ratio AB:AD in simplest form. Be sure that the quantities are in the same units.

  9. Find the measure of each angle. 6. Two supplementary angles have measures in the ratio 3:7. 7. The measures of the angles of a triangle are in the ratio 2:2:5. Solve 8. The perimeter of a triangle is 48 cm and the lengths of the sides are in the ratio 3:4:5. Find the length of each side.

  10. Homework pg. 243 CE #1-17 Odd WE # 1-33 odd, calc on 33

  11. Example A rectangular playing field has a length of one kilometer and a width of 520 meters. Find the ratio of the length to the width. Length Width 1000 520 25 13 4 = = ÷ 4 The ratio of length to width is 25 to 13, or 25:13

  12. Example Find the ratio of BC to AD. A B 120˚ 7 BC 6b 6b 14 14 AD 3b 70˚ 60˚ C D 7 The ratio of BC to AD: 3b

  13. Example Find the ratio of the measure of the smallest angle of the trapezoid to that of the largest angle. <B = 180 – 70 = 110 A B 110˚ 120˚ 120˚ Smallest angle: <D 6b 6b 14 14 Largest angle: <A 70˚ 1 m<D 60˚ 60˚ = = C D 2 m<A The ratio of smallest angle to largest angle: 1 to 2

  14. Example A telephone pole 7 meters tall snaps into two parts during a wind storm. The ratio of the two parts is 3:2. Find the length of each part. Let 3x and 2x be the two parts 3x 3x + 2x = 7 7 5x = 7 2x x = Then, 3x = 4.2 meters and2x = 2.8 meters. These are the lengths of the two parts of the telephone pole.

  15. Example The measures of the 5 interior angles of a pentagon are in the ratio 11:7:5:4:3. Find the measure of each angle. Let 11x, 7x, 5x, 4x and 3x be the measures of the angles The sum of the angles is (n-2)180, or (5-2)180. 11x + 7x + 5x + 4x + 3x = (5-2)180 30x = 540 x = 18 11(18) = 198 7(18) = 126 5(18) = 90 4(18) = 72 3(18) = 54 The angle measures are 198, 126, 90, 72 and 54.

  16. Proportion • an equation that states that two ratios are equal. • can be shown as: c d a b a:b = c:d or = first term third term second term fourth term

More Related