7-1 Vocabulary Ratio Proportion Extremes Means Cross products

7-1 Ratio and Proportion Geometry

7-1 Ratio A ratio is a comparison of two numbers with the same units by division. The ratio of 2 to 5 can be expressed three different ways; 2 to 5 2:5 2/5

Slope is a ratio, too Slope formula

Ex. 1 Write a ratio expressing the slope of AB.

Ratios A ratio can involve more than 2 numbers. Ex. 2) The ratio of the side lengths of a triangle is 4:7:5 and its perimeter is 96 cm. What is the length of the shortest side?

Cross Product Property of Proportions In a proportion, the product of the extremes(ad) is equal to the product of the means(bc). If , then ad = bc.

Ex. 3 Solve each proportion.  

Ratio’s (cont’d) Basically, a ratio has to be a comparison of only like labels (in., ft., yd., & mile) Referring to our previous example, then 2 ft to 5 ft we can write as a ratio, 2:5. If we had 3 ft. to 7 in., then we would have to change feet to inches first. 3 • 12 = ___ __ in. to 7 in. OR ___/7 36

Converting Ratios Ratios with different units, convert to same units first. Then simplify the fraction just like you would normally. Example 1 a) b)

Ex. 2 Find slope

Using Ratios Example 2 -The perimeter of the isosceles triangle shown is 56 in. The ratio of LM:MN is 5:4. Find the lengths of the sides and the base of the triangle.

Using extended ratios Example 3 – The measures of the sides in a triangle are in the extended ratio 4:7:5 & its perimeter is 96 cm. What is the length of the shortest side?

Application Ex. 4) Marla is making a scale drawing of her bedroom. Her rectangular room is 12 ½ feet wide and 15 feet long. On the scale drawing, the width of the room is 5 inches. What is the length?

Assignment

Ex. 4 The ratio of the measures of angles is 5:12:19. What is the measure of the largest angle?

Example 1- Solving Proportions a) b)

Example 2

Example 3

Example 4 A photo of a building has the measurements given in the sketch below. The actual building is 26¼ ft wide. How tall is it? What is the height of the door in the actual building?

Reciprocal Property If two ratios are equal, then their reciprocals are also equal. If then