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EXAMPLE 1

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

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EXAMPLE 1

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

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

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

  4. Blueprints The blueprint shows a scale drawing of a cell phone. The length of the antenna on the blueprint is5 centimeters. The actual length of the antenna is2 centimeters. What is the scale of the blueprint? length on blueprint 2.5 5 cm 2 2 5 2 length of antenna = = = 1 2 cm 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 is2.5 cm : 1 cm.

  5. RS ST MN NP = 10 8 = x 4 8 x = 4 10 8x = 40 x = 5 ANSWER The value ofxis 5 for Examples 1, 2 and 3 GUIDED PRACTICE 1.In Example1, find the value ofx. SOLUTION Write proportion Substitute. Cross Product property Multiply Divide

  6. BE BE = BC BC DE DE AC AC = = 18 + (18 + 6) = 42 AC 18 + 6 DE + AC 12 + AC BE + BC 22(12 + AC) = AC BC AC AC = 16 for Examples 1, 2 and 3 GUIDED PRACTICE 2.In Example2, find the value ofx. SOLUTION Given Property of Proportions (Property 4) Substitution Property of Equality Cross Products Property Solve for AC.

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

  8. length on blueprint 10 cm 10 2 5 = = = 2 cm 2 2 1 length of antenna for Examples 1, 2 and 3 GUIDED PRACTICE 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 is5 cm : 1 cm.

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