GEOMETRY Final Exam Review First Semester

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1 GEOMETRY Final Exam Review First Semester For questions 1-5, use the diagram shown as well as the word bank to complete each statement. In each case, list all that apply. Note: all terms in the word bank may not be used and some may be used more than once. 1. CH EJ 2. plane BAF plane AEJ 3. G, D, and I are points Word Bank: 4. E, K, and J are points A) parallel B) perpendicular C) skew 5. BG is to ED D) collinear E) coplanar F) concurrent 6. Point O is between points D and G. DO = 6, OG = 2x + 10 and DG = 24. Find the value of x. 7. Given the diagram and the fact that 8. Given the diagram, find m AEB. m ABC = 8x 10, find the value of x. Question 8 9. What is the perimeter of the rectangle 10. AB has endpoints A (-2, 3) and B (4, -1). shown? Find the midpoint AND the length of AB.

2 11. What is the next item in the pattern? 12. Determine whether the following conjecture 5, -15, 45, -135,... is true or false. Explain your answer. The product of any even number and 5 is always an odd number. 13. Write the A) converse, B) inverse, 14. Is the biconditional in question 13 true? C) contrapositive, and D) biconditional Explain your answer. of the following statement. If a segment connects the midpoint of two sides of a triangle, then it is parallel to the third side. 15. Use the diagram to identify the angle 16. If relationship for each pair of angles. A) 1 and 3 A) m 1 B) 2 and 7 B) m 5 C) 6 and 7 C) m 6 D) 1 and 5 D) m 8 o m 4 = 37, find the each measure. 17. Find the value of x in the diagram shown. 18. Find the value of x required for line m to be parallel to line n. 20. Find the equation of the line that is 21. Find the area and circumference of a circle perpendicular to y = 3x 1 and passes with a radius of 6 centimeters. through the point (6, 2). 22. Find the slope of the line through (1, 6) 23. Find an equation of the line that passes and (-3, 4). through the points (-2, 3) and (-6, 1).

3 24. Graph y = 3 5 x How many congruent sides does each type of have? A) Isosceles B) Scalene C) Equilateral 26. Find the value of x. Note: the triangle is 27. Find the value of x in the triangle shown. not drawn to scale. 28. Find m WTC in the diagram shown. 29. Given CAT DOG, name the segment or angle described. A) congruent to GO B) congruent to OGD C) congruent to TC 30. Which postulate or theorem can be used 31. Which postulate or theorem can be used to to prove that ABD CDB? Be sure to prove that the triangles in the diagram are mark your diagram to indicate additional congruent if C is the midpoint of AE and known congruencies. BD? Be sure to mark your diagram appropriately. Once you identify the postulate or theorem, state the congruent triangles. 32. Which postulate or theorem can be used to 33. Which postulate or theorem can be used to prove that the triangles in the diagram are prove that the triangles in the diagram are congruent? Be sure to mark your diagram congruent? Be sure to mark your diagram appropriately. Once you identify the appropriately. Once you identify the postulate or theorem, state the congruent postulate or theorem, state the congruent triangles. triangles.

4 34. Find the value o f x I the diagram shown. 35. Use the diagram to complete each statement. A) CD is the of AB. B) Ray EF is the of DEB. C) E is the of AB. 36. Complete the following proof. Statement Reason Given: BD bisects AE, AB DE 1. AB DE 1. given Prove: BC DC 2. A E vertical angles are congruent 4. BD bisects AE 4. given definition of a segment bisector Could three segments with lengths of 10 ft, 38. BX is the perpendicular bisector of AC. 13 ft, and 30 ft form a triangle? Show your What is the value of x? What is BC? work and explain your answer. 39. State the best name for each line. 40. SQ is a midsegment of NOP. What is A) AG B) CE C) DH the length of OP?

5 41. The lengths of two sides of a triangle are 42. State the range of possible values for x for 3 cm and 20 cm. What are all possible triangles shown. values for the length of the third side? 43. X, Y, and Z are all midpoints of their 44. Find the value of x in the triangle shown. respective sides. If MX = 6, WL = 8, and KW = 12, find the value of ZW, KY, and MW. 45. Is it possible to make a triangle with sides 46. Find the values of x and y in the triangles 8, 4, and 10? If it is, classify the triangle shown. by its angles. a. b. 47. Use the diagram to do each of the following. A) A town wants to build a beach house on a lake equidistant from the recreation center (R) and the school (S). Show point B where the beach house should be located. B) The town also wants to build a boatlaunching site that is equidistant from Elm Road and Main Street. Show point L were it should be built. C) On the diagram, locate the spot F for a flagpole that is to bhe the same distance from the recreation center, the school, and the courthouse (C).

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