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Geometry Review: Tools, Reasoning, and Proofs

This review focuses on fundamental geometry concepts such as tools of geometry, reasoning, and proofs. It includes questions related to geometric intersections, measurements, midpoints, and properties of segments. The review also covers collinearity and coplanarity of points, as well as the application of specific properties in geometric equations. Each question is answered with precise values and justifications where applicable, making it a comprehensive study guide for understanding and applying basic geometric principles.

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Geometry Review: Tools, Reasoning, and Proofs

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  1. Unit 1 Review Geometry: Tools of Geometry and Reasoning and Proof

  2. Question 1 Where do DCB and HIF intersect?

  3. Question 1 Answer

  4. Question 2 • If DM = 37 find the value of x.

  5. Question 2 Answer • X = 17

  6. Question 3 • Find the measure of

  7. Question 3 Answer • m=141

  8. Question 4 • What is the length of a segment with endpoints (-3, 5) and (4, 4)?

  9. Question 4 Answer

  10. Question 5 • What is the midpoint of the segment with endpoints (-2, 7) and (5, 2)?

  11. Question 5 Answer

  12. Question 6 • What is the other endpoint of a segment with an endpoint at (4,4) and a midpoint at (-2, -1)?

  13. Question 6 Answer • (-8, -6)

  14. Question 7 • Find the value of x and y:

  15. Question 7 Answer • X = 50 • Y=20

  16. Question 8 • Name the property that justifies each of the following: • If JK = 20 and AB +JK =XY, then AB + 20 = XY. • If , then HI GF

  17. Question 8 Answer • Substitution Property • Symmetric Property

  18. Question 9 • Name a pair of angles that form a linear pair:

  19. Question 9 Answer

  20. Question 10

  21. Question 10 Answer • = 28

  22. Question 11 • Find the

  23. Question 11 Answer • =138

  24. Question 12 • Find the value of x, if

  25. Question 12 Answer • X = 12

  26. Question 13 What are two other names for

  27. Question 13 Answer

  28. Question 14 • If G, H, and I are collinear and H is between G and I, GH = 7y + 3, HI = 3y − 5, and GI = 9y +7. Find the length of HI.

  29. Question 14 Answer • HI = 22

  30. Question 15 Find the length of KM if KL = and LM= 3x + 2.

  31. Question 15 Answer • KM = 8

  32. Question 16 • Find the midpoint and distance between the coordinates -4 and 9.

  33. Question 16 Answer • Midpoint: • Distance: 13

  34. Question 17 • Using the diagram name a: • Plane • Ray • Segment • Line

  35. Question 17 Answer • Possible answers: • Plane: ZRQ • Ray: • Segment: • Line:

  36. Question 18 • Name three Collinear Points

  37. Question 18 Answer • R, X, Q

  38. Question 19 • Name three coplanar points

  39. Question 19 Answer • Possible answers: • A, D, C • F, C, B • E, H, G

  40. Question 20 • Name the two planes that intersect at line DC:

  41. Question 20 Answer • ABC and HGC

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