Honors Geometry Term 1 Practice Final


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1 Name: Class: Date: ID: A Honors Geometry Term 1 Practice Final Short Answer 1. RT has endpoints R Ê Ë Á 4,2 ˆ, T Ê ËÁ 8, 3 ˆ. Find the coordinates of the midpoint, S, of RT. 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 Ê ËÁ 3,6 ˆ. 2. If m 3 = 68 û, find the measures of 5 and 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
2
3 Find the value of x. Use the diagram Point H is the? of the triangle. 25. CG is a(n)?,?,?, and? of ΔABC EF =? and EF Ä? by the? Theorem The vertices of ΔPQR are PÊ Ë Á 2,3 ˆ, Q Ê ËÁ 3,1 ˆ, and RÊ ËÁ 0, 3 ˆ. Decide whether ΔPQR is right, acute, or obtuse. 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
4 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 Ê ËÁ 1, 2 ˆ. 35. The line that is perpendicular to the line with equation y = 2x + 3 and passes through the point Ê ËÁ 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. 31. m 1 = 75 û. Find m isosceles Use the diagram to find the measure of the given angle. 37. acute 38. Find the perimeter of ΔBCD. 32. m 1 = 75 û. Find m m 1 = 75 û. Find m 8. 4
5 Use the diagram. Find the length of the segment HC 40. HB Use the figure to complete the statement. 41. HE 42. EF and 7 are? angles. 43. Name the special segments and the point of concurrency of the triangle and 5 are? angles. Find the value of x
6 49. 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 , 4, , 9, , 9, Use the triangle below. The midpoints of the sides of ΔABC are F, E, and D FD? If DE = 10, then AB =? 59. If the perimeter of ΔFDE is 18, then the perimeter of ΔABC is? 6
7 List the sides in order from shortest to longest. Complete the statement with the word inside, on, or outside In an acute triangle, the altitudes intersect the triangle. 65. In a right triangle, the altitudes intersect the triangle In an obtuse triangle, the altitudes intersect the triangle. Complete the statement with the word always, sometimes, or never. 67. The perpendicular bisectors of a right triangle will intersect outside the figure 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 be parallel to two sides of the triangle. 7
8 Complete the statement by writing <, =, or >. 73. m 1 m m ADC m ADB 74. m 5 m AB AC 8
9 Other Complete the proof. 75. Given: ABC ABD, ACB ADB Prove: ΔACB ΔADB 76. Write a twocolumn proof. Given: BD EC, AC AD Prove: AB AE Statements Reasons 1. ABC ABD ACB ADB AB AB ΔACB ΔADB 4. 9
10 77. Write a twocolumn proof. Given: SR bisects TSQ, T Q Prove: ΔRTS ΔRQS 10
11 ID: A Honors Geometry Term 1 Practice Final Answer Section SHORT ANSWER 1. S(2, 0.5) 2. m 5 = 68 û ;m 4 = 112 û 3. 2, 4, 6, 8 4. yes 5. y = 1 3 x 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 = x = x = x = centroid 25. median, perpendicular bisector, angle bisector, altitude 26. EF = 1 AB, EF Ä AB by the Midsegment Theorem acute 28. w = 11; PQ = 19; QR = m PQT = 65 û by the Congruent Complements Theorem 31. m 2 = 105 û 32. m 5 = 75 û 33. m 8 = 75 û 1
12 ID: A 34. y = 2x y = 1 2 x 36. ΔQPS and ΔQSR 37. ΔQPS angle bisectors; incenter 44. perpendicular bisectors; circumcenter 45. medians; centroid 46. alternate exterior angles 47. alternate interior angles yes 55. no 56. no 57. BE and CE QR, RS, QS 61. AC, CB, AB 62. RS, RT, ST 63. RT 64. inside 65. on 66. outside 67. never 68. always 69. never 70. never 71. < 72. > 73. > 74. < 2
13 ID: A OTHER 75. Statements Reasons 1. ABC ABD 1. Given 2. ACB ADB 2. Given 3. AB AB 3. Reflexive property 4. ΔACB ΔADB 4. AASTheorem Statements Reasons 1. BD EC, AC AD 1. Given Base angles of an isoceles triangle are congruent. 3. ABD AEC 3. SASCongruence Postulate 4. AB AE Statements 4. Corresponding parts of congruent Reasons triangles are congruent. 1. SR bisects TSQ 1. Given Def. of angle bisector 3. T Q 3. Given 4. RS RS 4. Reflexive prop. of congruence 5. ΔRTS ΔRQS 5. AASCongruence Post. 3
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