Use the image below and the Segment Addition Postulate to find the missing values.1. If 𝐸𝐹―=9 𝑎𝑛𝑑 𝐹𝐺―=15, 𝑡ℎ𝑒𝑛 𝐸𝐺―= 2. If 𝐸𝐹―=2𝑥−2, 𝐹𝐺―=3𝑥+1, 𝑎𝑛𝑑 𝐸𝐺―=64, find the value of 𝑥, then find 𝐸𝐹― 𝑎𝑛𝑑 𝐹𝐺― 𝑥= 𝐸𝐹―= 𝐹𝐺―=
Question
Use the image below and the Segment Addition Postulate to find the missing values.1. If 𝐸𝐹―=9 𝑎𝑛𝑑 𝐹𝐺―=15, 𝑡ℎ𝑒𝑛 𝐸𝐺―= 2. If 𝐸𝐹―=2𝑥−2, 𝐹𝐺―=3𝑥+1, 𝑎𝑛𝑑 𝐸𝐺―=64, find the value of 𝑥, then find 𝐸𝐹― 𝑎𝑛𝑑 𝐹𝐺― 𝑥= 𝐸𝐹―= 𝐹𝐺―=
Solution
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The Segment Addition Postulate states that if a line segment has three points, then the sum of the lengths of the two smaller segments equals the length of the larger segment. So, if EF = 9 and FG = 15, then EG = EF + FG = 9 + 15 = 24.
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If EF = 2x - 2, FG = 3x + 1, and EG = 64, then according to the Segment Addition Postulate, EG = EF + FG. So, we can set up the equation 64 = 2x - 2 + 3x + 1. Simplifying this equation gives 64 = 5x - 1. Solving for x gives x = 13.
Substituting x = 13 into the expressions for EF and FG gives EF = 2(13) - 2 = 24 and FG = 3(13) + 1 = 40.
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