19. This problem will prepare you for the Multi-Step Test Prep on page 34. Archaeologists at Valley Forge were eager to find what remained of the winter camp that soldiers led by George Washington called home for several months. The diagram represents one of the restored log cabins. _ a. How is C related to AE? b. If AC = 7 ft, EF = 2(AC) + 2, and AB = 2(EF) - 16, what are AB and EF?
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Use the diagram for Exercises 20–23. 2 . Find GH. 20. GD = 4_ 3 _ _ _ 21. CD ≅ DF, E bisects DF, and CD = 14.2. Find EF.
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22. GH = 4x - 1, and DH = 8. Find x. _
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23. GH bisects CF, CF = 2y - 2, and CD = 3y - 11. Find CD. Tell whether each statement is sometimes, always, or never true. Support each of your answers with a sketch. 24. Two segments that have the same length must be congruent. _
25. If M is between A and B, then M bisects AB. 26. If Y is between X and Z, then X, Y, and Z are collinear. 27.
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Below are two statements about the midpoint of AB. Which is incorrect? Explain the error. �
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28. Carpentry A carpenter has a wooden dowel that is 72 cm long. She wants to cut it into two pieces so that one piece is 5 times as long as the other. What are the lengths of the two pieces? 29. The coordinate of M is 2.5, and MN = 4. What are the possible coordinates for N? 30. Draw three collinear points where E is between D and F. Then write an equation using these points and the Segment Addition Postulate. Suppose S is between R and T. Use the Segment Addition Postulate to solve for each variable. 31. RS = 7y - 4 ST = y + 5 RT = 28
32. RS = 3x + 1 1x + 3 ST = _ 2 RT = 18
33. RS = 2z + 6
ST = 4z - 3 RT = 5z + 12
34. Write About It In the diagram, B is not between A and C. Explain. 35. Construction Use a compass and straightedge to construct a segment whose length is AB + CD.
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Chapter 1 Foundations for Geometry
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