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Name: ______________________ Class: _________________ Date: _________ ID: A Honors Geometry Term 1 Practice Final Short Answer 5. Line p 1 has equation y = −3x + 5. Write an equation of line p 2 which is perpendicular to p 1 and passes through the point ÊÁË −3, 6 ˆ˜¯ . 1. RT has endpoints R ÊÁË −4, 2 ˆ˜¯ , T ÊÁË 8, − 3 ˆ˜¯ . Find the coordinates of the midpoint, S, of RT. 2. If m∠3 = 68 û , find the measures of ∠5 and ∠4. 6. In ΔABC, the measure of ∠A = 116 û . The measure of ∠B is three times the measure of ∠C. Find m∠B and m∠C. 3. If l Ä m, which angles are supplementary to ∠1? Decide whether it is possible to prove that the triangles are congruent. If it is possible, tell which congruence postulate or theorem you would use. Explain your reasoning. 7. Decide whether lines p 1 and p 2 are perpendicular. 4. 8. 1 ID: Version 9. 15. 10. 16. 11. 17. 12. 18. 13. 19. 14. 2 ID: Version Find the value of x. Use the diagram. 20. 24. Point H is the ? of the triangle. 21. 25. CG is a(n) ? , ? , ? , and ? 22. 26. EF = ? and EF Ä ? by the ? of ΔABC. Theorem. 27. The vertices of ΔPQR are P ÊÁË −2, 3 ˆ˜¯ , Q ÊÁË 3, 1 ˆ˜¯ , and R ÊÁË 0, − 3 ˆ˜¯ . Decide whether ΔPQR is right, acute, or obtuse. 23. 28. Q is between P and R. PQ = 2w − 3, QR = 4 + w, PR = 34. Find the value of w. Then find the lengths of PQ and QR. 29. Suppose m∠PQR = 130 û . If QT bisects ∠PQR, what is the measure of ∠PQT? 3 ID: Version 30. A tool and die company produces a part that is to be packed in triangular boxes. To maximize space and minimize cost, the boxes need to be designed to fit together in shipping cartons. If ∠1 and ∠2 have to be complementary, ∠3 and ∠4 have to be complementary, and m∠2 = m∠3, describe the relationship between ∠1 and ∠4. Write an equation of the line described. 34. The line that is parallel to the line with equation y = −2x + 3 and passes through the point ÊÁ −1, − 2 ˆ˜ . Ë ¯ 35. The line that is perpendicular to the line with equation y = −2x + 3 and passes through the point ÁÊË −2, − 1 ˜ˆ¯ . Use the diagram to find the measure of the given angle. Identify all triangles in the figure that fit the given description. 36. isosceles 31. m∠1 = 75 û . Find m∠2. 37. acute Use the diagram to find the measure of the given angle. 38. Find the perimeter of ΔBCD. 32. m∠1 = 75 û . Find m∠5. 33. m∠1 = 75 û . Find m∠8. 4 ID: Version Use the diagram. Find the length of the segment. 44. 45. 39. HC 40. HB Use the figure to complete the statement. 41. HE 42. EF 46. ∠2 and ∠7 are ? angles. Name the special segments and the point of concurrency of the triangle. 47. ∠4 and ∠5 are ? angles. 43. Find the value of x. 48. 5 ID: Version Determine whether it is possible to draw a triangle with sides of the given lengths. Write yes or no. If yes, determone the type of trinagle it is: acute, right or obtuse and scalene, isosceles or equilateral. 49. 54. 3, 4, 5 55. 4.7, 9, 4.1 50. 56. 4, 9, 13 Use the triangle below. The midpoints of the sides of ΔABC are F, E, and D. 51. 52. 57. FD ≅ __________? 58. If DE = 10, then AB = __________ ? 53. 59. If the perimeter of ΔFDE is 18, then the perimeter of ΔABC is _______? 6 ID: Version List the sides in order from shortest to longest. Complete the statement with the word inside, on, or outside. 60. 64. In an acute triangle, the altitudes intersect the triangle. 65. In a right triangle, the altitudes intersect the triangle. 66. In an obtuse triangle, the altitudes intersect the triangle. 61. Complete the statement with the word always, sometimes, or never. 67. The perpendicular bisectors of a right triangle will intersect outside the figure. 62. 68. The medians of an obtuse triangle will intersect inside the triangle. 69. The perpendicular bisectors of an obtuse triangle will intersect on the triangle. 63. In ΔXYZ and ΔRST, which is longer, XZ or RT? 70. The midsegment of a triangle will parallel to two sides of the triangle. 7 be ID: Version Complete the statement by writing < , = , or >. 71. m∠ADC 72. AB 73. m∠1 m∠2 74. m∠5 m∠6 m∠ADB AC 8 ID: Version Other Complete the proof. Write a two-column proof. 75. Given: ∠ABC ≅ ∠ABD, ∠ACB ≅ ∠ADB 76. Given: BD ≅ EC, AC ≅ AD Prove: ΔACB ≅ ΔADB Prove: AB ≅ AE Statements Reasons 1. ∠ABC ≅ ∠ABD 1. __________________ 2. ∠ACB ≅ ∠ADB 2. __________________ 3. AB ≅ AB 3. __________________ 4. ΔACB ≅ ΔADB 4. __________________ 9 ID: Version 77. Write a two-column proof. Given: SR bisects ∠TSQ, ∠T ≅ ∠Q Prove: ΔRTS ≅ ΔRQS 10 ID: A Honors Geometry Term 1 Practice Final Answer Section SHORT ANSWER 1. 2. 3. 4. S(2, 0.5) m∠5 = 68 û ;m∠4 = 112 û ∠2, ∠4, ∠6, ∠8 yes 1 5. y = x + 7 3 6. m∠C = 16 û , m∠B = 48 û 7. Yes; ASA Congruence Postulate. Since ∠LMP ≅ ∠NPM and ∠NMP ≅ ∠LPM (given), and MP ≅ MP (reflexive property of congruence), two pairs of corresponding angles are congruent and two corresponding included sides are congruent. 8. no 9. yes; HL Theorem 10. yes; SAS 11. no 12. yes; ASA 13. yes; SSS 14. No; only one common side and one set of corresponding angles are congruent. 15. Yes; SAS, reflexive property, two pairs of corresponding sides and the included angles are congruent. 16. Yes; SSS, reflexive property and three pairs of corresponding sides are congruent. 17. Yes; AAS, vertical angles are congruent, one other pair of corresponding angles and one pair of corresponding sides are congruent. 18. No; only two pairs of corresponding angles are congruent. 19. Yes; SAS, two pairs of corresponding sides and the angles included are congruent. 20. x = 7 21. x = 22.5 22. x = 55 23. x = 5 24. centroid 25. median, perpendicular bisector, angle bisector, altitude 1 26. EF = AB, EF Ä AB by the Midsegment Theorem. 2 27. acute 28. w = 11; PQ = 19; QR = 15 29. 30. 31. 32. 33. m∠PQT = 65 û ∠1 ≅ ∠4 by the Congruent Complements Theorem m∠2 = 105 û m∠5 = 75 û m∠8 = 75 û 1 ID: A 34. y = −2x − 4 1 35. y = x 2 36. ΔQPS and ΔQSR 37. ΔQPS 38. 64 39. 12 40. 10 41. 5 42. 8 43. angle bisectors; incenter 44. perpendicular bisectors; circumcenter 45. medians; centroid 46. alternate exterior angles 47. alternate interior angles 48. 13 49. 21 50. 1 51. 20 52. 45 53. 78 54. yes 55. no 56. no 57. BE and CE 58. 20 59. 36 60. QR, RS, QS 61. AC, CB, AB 62. RS, RT, ST 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. RT inside on outside never always never never < > > < 2 ID: A OTHER 75. 76. Statements Reasons 1. ∠ABC ≅ ∠ABD 1. Given 2. ∠ACB ≅ ∠ADB 2. Given 3. AB ≅ AB 3. Reflexive property 4. ΔACB ≅ ΔADB 4. AAST heorem Statements Reasons 1. BD ≅ EC, AC ≅ AD 1. Given 2. ∠1 ≅ ∠2 2. Base angles of an isoceles triangle are congruent. 3. ABD ≅ AEC 4. AB ≅ AE 3. SASCongruence Postulate 4. Corresponding parts of congruent triangles are congruent. 77. Statements Reasons 1. SR bisects ∠TSQ 1. Given 2. ∠1 ≅ ∠2 2. Def. of angle bisector 3. ∠T ≅ ∠Q 3. Given 4. RS ≅ RS 4. Reflexive prop. of congruence 5. ΔRTS ≅ ΔRQS 5. AASCongruence Post. 3