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Fundamentals of Geometry: Finding Values and Triangle Properties

This chapter covers essential concepts in geometry, including solving for unknown values (x) in various geometric equations, understanding midsegments of triangles, and calculating perimeter and side lengths. Explore the relationships between triangle sides and angles, including properties of isosceles triangles and medians. Learn to identify perpendicular bisectors, centroids, and order sides and angles based on given measurements. Gain practical skills in problem-solving related to geometric figures and their properties.

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Fundamentals of Geometry: Finding Values and Triangle Properties

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  1. GeometryChapter 5Sections 5-1 to 5-5

  2. Chapter 5 Geometry 500

  3. Find the value of x. 5x 10 A

  4. 2(10) = 5x or 10 = 5x/2 What is x = 4?

  5. Find the value of x. 24 6x A

  6. 24 2 = 6x What is x = 8?

  7. Given segment FB is the midsegment of triangle GDA and segment EC is the midsegment of triangle FDB. The lengths of segments GA and EC are these. G F E 9 D A B C A

  8. What are 18 and 4.5?

  9. If segment VR = 12, segment WS =5, segment SR =7. This is the perimeter of triangle VTR. U V T S W R A

  10. What is P = 36?

  11. Given: Perimeter = 44. Find the value of x. 4x x+5 2x+3 A

  12. 2(4x) + 2(2x+3) + 2 (x+5) What is x = 2?

  13. Segment RT = 20; Segment RS = 10; Segment SU = 10. The lengths of segments WU and RU are these. S W R T U A

  14. What is 5 and 10?

  15. Find the value of x. 4x 3x+10 A

  16. 4x = 3x + 10 What is x = 10?

  17. How is segment GI related to segment HJ? H K G I J A

  18. What is a perpendicular bisector?

  19. Find the value of x. 7x – 1 4x + 5 A

  20. What is x = 2?

  21. The type of triangle that triangle ABD represents. B 3 1 E A C 1 3 D A

  22. What is an Isosceles triangle?

  23. Segment QS Q S A

  24. What is a median of the triangle?

  25. Segment QS Q S A

  26. What is a perpendicular bisector?

  27. Segment QS Q S A

  28. What is an altitude of the triangle?

  29. The point of concurrency of the medians of a triangle. A

  30. What is the centroid?

  31. Points B, D, and F are midpoints of segments AC, CE, and EA, respectively. G is the point of concurrency of the medians. Segment AG measures 12 cm. The lengths of segments GD and AD are these. C B D G A E F A

  32. What are 6 and 18?

  33. The negation of: Today is sunny. A

  34. What is Today is not sunny?

  35. The inverse of this conditional statement: If a figure is a square, then it has four sides. A

  36. What is If a figure is not a square, then it does not have four sides.

  37. The contrapositive of this conditional statement: If a figure is a triangle, then it has three sides. A

  38. What is If a figure does not have three sides, then it is not a triangle?

  39. Its symbolic representation is: ~q  ~p A

  40. What is a contrapositive?

  41. Its symbolic representation is: ~p A

  42. What is a negation?

  43. List the sides of triangle DEF in order from shortest to longest. E 79 25 D F A

  44. What are segments DE, EF, and DF?

  45. Given: Triangle RST with mR = 39 and mS = 87. List the sides in order from shortest to longest. A

  46. What are segments ST, RS, and TR?

  47. Triangle LMO has side lengths LM = 14, MO = 12, OL = 10. List the angles of the triangle from largest to smallest. A

  48. What are O, L, and M?

  49. Triangle JKL has side lengths as shown. List the angles from smallest to largest. K 2.1 cm 0.027 m J L 23,000 mm A

  50. What are L, K, and J?

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