Sandia High School Geometry First Semester FINAL EXAM
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1 Sandia High School Geometry First Semester FINL EXM Name: Part I: Multiple hoice. Write the letter of the single, correct answer to each problem on the left of the problem. (Each problem is worth 1 point.) Problems 1-4: Use the following choices:.... E. 1. Which picture best illustrates the following postulate? The intersection of two planes is a line. 2. Which picture best illustrates the following postulate? If two points are in a plane, then the line containing them is in that plane. 3. Which picture best illustrates the fact that the intersection of three planes can be a line? 4. Which picture best illustrates the fact that the intersection of a line and a plane can be a single point? 5. Which three points in the figure on the right are collinear? G H. G, K and Q. H, K and P. H, K and R. K, P and R P K Q E. G, P and T R T Geometry: First Semester Final Exam Page 1 of 12
2 Problems 6-8: The figure on the right is a 3-dimensional drawing of a shed with no doors or windows. Its roof, sides and floor are parts of seven H Q G P different planes. Planes and EFG (containing the front and back walls) are parallel, as are planes H and G (containing the left and right walls). No other planes determined by the roof, E F walls or floor of this shed are parallel. 6. Which of the following points is coplanar with points H, Q and P?. point. point. point. point E. point E 7. Name the intersection of plane HQP with plane.. P. point P. P. point E. PQ 8. What geometric object is the intersection of with plane HQP?. a line. a point. a plane. a puppy E. a banana 9. Which is NOT a valid name for the angle depicted on the right? K. KPN. MPK. P. KNP E. 1 P 1 M N 10. Which of these angles has a measure closest to 30 o?.... E. Geometry: First Semester Final Exam Page 2 of 12
3 11. In the figure on the right, points P, Q and R are collinear. What is the measure of RQS?. 40 o. 20 o. 80 o. 50 o E. 100 o S (5x) o (4x) o P Q R 12. If and are complementary, and are supplementary, and m = 64 o, then what is the measure of?. 64 o. 180 o. 26 o. 90 o E. 154 o 13. In this figure, m O = 70, m O = 60, and m O = 100. What is m O?. 10 o. 65 o. 35 o. 60 o E. 30 o O Problems 14-16: Refer to the figure on the right, in which M, R and Q are collinear and m MRN = 90 : M N 14. Which of the following is a straight angle?. MRN. PMR. MRQ. PRN E. NTR P R Q T 15. Which of the following is an obtuse angle?. MRQ. PRN. NTR. MRN E. PMR 16. Which of the following angles is adjacent to NRT?. QRT. MRT. PRM. PRN E. PMR Geometry: First Semester Final Exam Page 3 of 12
4 17. In which of the following diagrams is it true that GQ + RQ = GR?.. G R Q R Q G. R G Q. G E. Q R G Q R 18. Point P (not shown) on the number line is 5 units from point T and 3 units from point S R O S T Where is point P located?. etween R and O. etween O and S. etween S and T. To the left of R E. To the right of T 19. Towns, and are located along a straight highway. Town is between and, and the distance from to is 17 miles more than the distance from to. If and are 95 miles apart, how far is it from town to town?. 42 miles. 29 miles. 56 miles. 45 miles E. 39 miles 20. The process of making a conjecture based on a series of observed patterns is known as. deductive reasoning. obfuscation. proof. inductive reasoning E. brawling 21. When a conjecture has been proved, it becomes a. postulate. diagram. theorem. definition E. assertion Geometry: First Semester Final Exam Page 4 of 12
5 22. Which of the following is the converse of the statement, if a quadrilateral is a square, then its four sides are congruent?. If the four sides of a quadrilateral are congruent, then it is a square.. If a square is a quadrilateral, then its four sides are congruent.. If the four sides are congruent, then it is a quadrilateral square.. If four sides are congruent, then the square is a quadrilateral. E. If a square has four congruent sides, then it is a quadrilateral 23. The figure on the right is a rhombus. Which of the following statements about it is NOT true?. Its diagonals bisect each other.. Its diagonals are congruent.. Its diagonals are perpendicular.. Each pair of opposite angles are congruent. E. Each pair of consecutive angles are supplementary. 24. Which of the following figures is a counterexample to the false statement, if the diagonals of a quadrilateral are congruent and bisect each other, then the quadrilateral is a square?.... E. Geometry: First Semester Final Exam Page 5 of 12
6 25. Given quadrilateral, which statement would allow the conclusion that is a parallelogram?... m + m = 180. E. None of these 26. Which of the following statements is always true regarding a parallelogram?. The diagonals are perpendicular to each other.. The sum of the angles is 180 o.. Opposite sides are both parallel and congruent.. There cannot be a right angle in any parallelogram. E. onsecutive angles are complementary. Problems 27-29: In the figure on the right, lines m and n are cut by transversal t. m t and 5 are:. corresponding angles. vertical angles n alternate interior angles. alternate exterior angles E. same side exterior angles and 5 are:. corresponding angles. vertical angles. alternate interior angles. alternate exterior angles E. same side exterior angles and 7 are:. corresponding angles. vertical angles. alternate interior angles. alternate exterior angles E. same side exterior angles Geometry: First Semester Final Exam Page 6 of 12
7 30. In the figure on the right, lines m and n are t parallel. Find m 8. m (8x 3) o. 45 o. 117 o. 75 o. 135 o E. 113 o n (2x + 33) o In the triangle on the right, m P = 25. What is the measure of Q? Q. 75 o. 105 o. 55 o. 25 o E. 65 o R P 32. What is the measure of in this triangle?. 49 o. 41 o. 131 o?. 139 o E. 141 o 21 o 28 o 33. In a quadrilateral, two of the angles each have a measure of 110 o, and the measure of a third angle is 90 o. What is the measure of the remaining angle?. 50 o. 130 o. 90 o. 140 o E. None of these 34. EF is a regular hexagon. What is the measure of?. 108 o. 72 o. 120 o F. 60 o E. 144 o E 35. In the pentagon at the right, what is the value of x? o x o. 158 E o 90 o 50 o Geometry: First Semester Final Exam Page 7 of 12
8 36. What is the area of the triangle on the right?. 18 in in in 2 4 in. 13 in 2 E. 26 in 2 9 in 37. How many triangles of the shape and size of the shaded triangle can the trapezoid on the right be divided into?. three. seven. four. five E. six What is the area of the shaded square on the right?. 24 cm 2. 9 cm cm cm 2 E. 72 cm 2 6 cm 6 cm 39. What is the area of the trapezoid on the right? 5 cm. 48 cm cm cm cm 2 E. 20 cm 2 11 cm 7 cm 40. square has an area of 196 in 2. What is the perimeter of that square?. 24 in. 48 in. 56 in. 392 in E. 28 in 41. Which is closest to the area of the shaded region in the figure on the right?. 206 ft ft ft ft 2 E. 55 ft 2 16 ft Geometry: First Semester Final Exam Page 8 of 12
9 42. If the slope a certain line is 2, then which of the following is the slope of a line 3 perpendicular to that line? E. 3 Problems 43-46: Use the following choices for the two triangles given.. The triangles are congruent by SS.. The triangles are congruent by S.. The triangles are congruent by SSS.. The triangles are congruent by S. E. The triangles might not be congruent and : Geometry: First Semester Final Exam Page 9 of 12
10 Part II: Written. Show all work. (Each problem is worth 5 points.) 47. In the figure below, =, =, = 2, and = 132. What is the length of? 48. In, E, m = 82, m = 35, and m = 32. Find the indicated angle 82 o measures: E m E = m E = 35 o 32 o m E = 49. If TUV, m V = x o, U V = y, m = 80 o, and UV = 13, find the values of x and y. T 50. Find the value of x: x Geometry: First Semester Final Exam Page 10 of 12
11 Problems 51-52: The vertices of quadrilateral EFGH have the following coordinates: E = (6, 3) F = (10, 11) G = ( 10, 5) H = (0, 7) Points M, N, P, and Q are the midpoints of sides EF, FG, GH, and HE, respectively. 51. raw quadrilateral EFGH, give the coordinates of its midpoints, and draw quadrilateral MNPQ: y x Give the coordinates of the midpoints: M = midpoint of EF = P = midpoint of GH = N = midpoint of FG = Q = midpoint of EH = 52. (a) Prove that quadrilateral MNPQ is a parallelogram by showing its opposite sides have the same slopes: slope of MN =, slope of PQ =, slope of NP =, slope of MQ = (b) Is MNPQ a rectangle? Why or why not? Geometry: First Semester Final Exam Page 11 of 12
12 53. Mark the diagram and supply the missing reasons for the proof: Given:, P bisects Prove: P Proof: Statement: Reason: Given P P P bisects Given P P P P P P Geometry: First Semester Final Exam Page 12 of 12
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