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EXAMPLE 3

Use the diagram to find GH. FH. =. FG + GH. 36. 21 + GH. =. 15. GH. =. EXAMPLE 3. Find a length. SOLUTION. Use the Segment Addition Postulate to write an equation. Then solve the equation to find GH. Segment Addition Postulate. Substitute 36 for FH and 21 for FG.

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EXAMPLE 3

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  1. Use the diagram to find GH. FH = FG+ GH 36 21+GH = 15 GH = EXAMPLE 3 Find a length SOLUTION Use the Segment Addition Postulate to write an equation. Then solve the equation to find GH. Segment Addition Postulate. Substitute 36 for FHand 21 for FG. Subtract 21 from each side.

  2. To find the length of a horizontal segment, find the absolute value of the difference of the x-coordinates of the endpoints. JK = 2 – (– 3) = 5 EXAMPLE 4 Compare segments for congruence Plot J(– 3, 4), K(2, 4), L(1, 3), and M(1, – 2) in a coordinate plane. Then determine whether JKand LMare congruent. SOLUTION Use Ruler Postulate.

  3. LM = – 2 – 3 = 5 ~ JKand LMhave the same length. So, JK LM. = ANSWER EXAMPLE 4 Compare segments for congruence To find the length of a vertical segment, find the absolute value of the difference of the y-coordinates of the endpoints. Use Ruler Postulate.

  4. 5. Use the diagram at the right to find WX. 144 = 37 + wx = wx 107 ANSWER WX = 107 for Examples 3 and 4 GUIDED PRACTICE Use the segment addition postulate to write an equation. Then solve the equation to find WX SOLUTION vx = vw + wx Segment addition postulate Substitute 37 for vw and144for vx Subtract 37 from each side

  5. Plot the points A(– 2, 4),B(3, 4), C(0, 2), and D(0, – 2) in a coordinate plane. Then determine whether ABand CDare congruent. Length of AB is not equal to the length of CD, so they are not congruent ANSWER for Examples 3 and 4 GUIDED PRACTICE 6.

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