7 1 Vocabulary Ratio Proportion Extremes Means Cross

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. • A(-1, 3), B(2, -2)

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

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