1. EXAMPLE 1 Use properties of proportions SOLUTION NP ST MN RS = Because 4 x = 8 10, then In the diagram, NP ST MN RS = Write four true proportions. By the Reciprocal Property, the reciprocals are equal, so x 4 = 10 8 By Property 3, you can interchange the means, so = 8 4 10 x

2. EXAMPLE 1 Use properties of proportions By Property 4, you can add the denominators to the numerators, so 8 + 10 10 4 + x x x =, or 18 10 =.

3. EXAMPLE 2 Use proportions with geometric figures Given Property of Proportions (Property 4 ) Substitution Property of Equality Cross Products Property Solve for x. BE EC BD DA = SOLUTION 18 + 6 6 = x 3 x 12 = 6x6x3(18 + 6) = So, BA = 12 and BD = 12 – 3 = 9. ALGEBRA In the diagram, BE EC BD DA = Find BA and BD. = BE + EC EC BD + DA DA

4. EXAMPLE 3 Find the scale of a drawing SOLUTION To find the scale, write the ratio of a length in the drawing to an actual length, then rewrite the ratio so that the denominator is 1. The scale of the blueprint is 2.5 cm : 1 cm. = 5 cm 2 cm = 5 2 2 = 2.5 1 The blueprint shows a scale drawing of a cell phone. The length of the antenna on the blueprint is 5 centimeters. The actual length of the antenna is 2 centimeters. What is the scale of the blueprint? Blueprints length on blueprint length of antenna

5. GUIDED PRACTICE for Examples 1, 2 and 3 1. In Example 1, find the value of x. RS ST MN NP = SOLUTION Write proportion 10 x = 8 4 Substitute. = 8 x4 10 8x8x =40 Cross Product property Multiply x =5 Divide ANSWER The value of x is 5

6. GUIDED PRACTICE for Examples 1, 2 and 3 2. In Example 2, find the value of x. SOLUTION BE BC DE AC = Given Property of Proportions (Property 4 ) Substitution Property of Equality Cross Products Property Solve for AC. BE BC DE AC = = BE + BC BC DE + AC AC 16= = 12 + AC AC 18 + (18 + 6) 18 + 6 = 22(12 + AC)42 AC

7. GUIDED PRACTICE for Examples 1, 2 and 3 ANSWER So, AC = 16

8. GUIDED PRACTICE for Examples 1, 2 and 3 3. What If ? In Example 3, suppose the length of the antenna on the blueprint is 10 centimeters. Find the new scale of the blueprint. SOLUTION To find the scale, write the ratio of a length in the drawing to an actual length, then rewrite the ratio so that the denominator is 1. The scale of the blueprint is 5 cm : 1 cm. length on blueprint length of antenna = 10 cm 2 cm 10 2 = 2 = 5 1