# Geometry - Semester 1 Final Review Quadrilaterals

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1 Geometry - Semester 1 Final Review Quadrilaterals 1. Consider the plane in the diagram. Which are proper names for the plane? Mark all that apply. a. Plane L b. Plane ABC c. Plane DBC d. Plane E e. Plane EDL Name: Per: Date: 2. Which diagram does not show plane ABC? a. b. c. d. 3. Which diagram does not show CD bisecting AB? a. b. c. 4. Which two angles are vertical angles in the diagram? a. AEB and CED b. E and E c. AC and DB d. AED and CEB 5. Which two angles make a linear pair in the same diagram? a. AEB and CED b. AEC and BED c. AED and CEA d. AED and CEB

2 6. In the diagram on the right 1 2 3, and m CEB = 55, m DEL = 65. Which of the following cannot be concluded? a. KLE 1 b. AB FG c. CD KH d. BEL ELK 7. In the diagram on the right, lines n and m are cut by transversals p and q. Which value of x would make lines n and m parallel? a. 110 b. 80 c. 70 d Two angles are supplementary. What can be concluded about them? a. They are both acute. b. They are both obtuse. c. They cannot be both right. d. Either they are both right, or one is acute and one is obtuse. 9. Two angles are complementary. What can be concluded about them? a. They are both acute. b. They are both obtuse. c. They are both right. d. Either they are both right, or one is acute and one is obtuse. 10. If m TUY = 90 and m YUV = 55, find m TUV. 11. If m TUV = 150 and m YUV = 48, find m TUY. 12. If m ABC = 130, m ZBC = x and m ABZ = x + 29, find x. 13. Find m ABC if m ABZ = 37x + 1, m ZBC = 110, and m ABC = 147x Find JM 15. A, B, C are collinear and B is between A and C. Find x if AC = 8, BC = x 2, and AB = x Find the midpoint between A and B. a. 3 b. 2 c. 1.5 d Which of the following starts with If a transversal crosses two parallel lines? (Mark all that apply) a. Corresponding Angles b. Alternate Interior Angles d. Same Side Interior Angles e. Same Side Exterior Angles f. Converse of Corresponding Angles c. Alternate Exterior Angles g. Converse of Alternate Interior Angles h. Converse of Alternate Exterior Angles

3 i. Converse of Same Side Interior Angles j. Converse of Same Side Exterior Angles 18. Which of the following starts with If the <adjective> angles are? (Mark all that apply) a. Corresponding Angles f. Converse of Corresponding Angles b. Alternate Interior Angles c. Alternate Exterior Angles g. Converse of Alternate Interior Angles h. Converse of Alternate Exterior Angles d. Same Side Interior Angles i. Converse of Same Side Interior Angles e. Same Side Exterior Angles j. Converse of Same Side Exterior Angles 19. On a separate paper: a. State and prove the alternate interior angles theorem. b. State and prove the converse of the alternate interior angles theorem. 20. In the right triangle ABC, with m B = 90, the hypotenuse is AC = 16cm. BD AC, and CD = 7cm. Find the length of BD. a. BD = 3 7 b. BD = 4 7 c. BD = 7 3 d. BD = The coordinates of the endpoints of AB are A(0, 0) and B(0, 6). What is the equation of the perpendicular bisector of AB? a. x = 0 b. x = 3 c. y = 0 d. y = The diagram shows isosceles triangle ABC. What is the value of x? a. 10 b. 28 c. 32 d Which of the lines is parallel to the line y = 4x + 7 and passes through the point ( 4,2)? a. y = Q x + 3 c. y = Q x + 2 R R b. y = 4x + 2 d. y = 4x What is the equation of a line passing through (2,1) and parallel to the line y = 2x + 1? a. y = Q x c. y = 2x 5 S b. y = Q x + 1 d. y = 2x 1 S 25. Which of the following is perpendicular to a line with slope Q T? a. y = Q T x b. y = 3x + 5 c. y = 3x 1 d. y = Q T x Which is an equation of a perpendicular bisector to PQ, where P( 2,5) and Q(6, 3). a. y = x + 3 c. y = x 1 b. y = x + 3 d. y = x Which is an equation of a perpendicular bisector to RS, where R(8,2) and S(0,6). a. y = 2x 4 b. y = Q S x + 2 c. y = Q S x + 6 d. y = 2x Point M is the midpoint of AB. If A( 3,6) and M( 5,2), what are the coordinates of B?

4 a. (1,2) b. (7,10) c. (-4,4) d. (-7,-2) 29. In the diagram on the right A Y B Y C Y is the image of ABC and A YY B YY C YY is the image of A B C. The combined transformation mapping ABC onto A YY B YY C YY is an example of: a. Reflection followed by a rotation. b. Reflection followed by a translation. c. Translation followed by a rotation. d. Translation followed by a reflection. 30. Describe the transformation mapping ABC onto A B C specifically (verbally, or using function notation). 31. Parallelogram ABCD has vertices A 2,0, B 0, 3, C 3, 3, and D(5,0) a. Use slopes to show that it is indeed a parallelogram. b. If it is reflected across the x-axis, how many vertices would stay at their original position? 32. What are the coordinates of (3,4) reflected across the line y = x? a. ( 4, 3) b. ( 3,4) c. (4, 3) d. (4,3) 33. In FGH, m F = 41 and m H = 102. What is m G? a. 47 b. 61 c. 143 d ACD is isosceles with AC CD. If m A = 36 and m BCD = 19. Find m B. a. 17 b. 19 c. 36 d In DEF, m D = 3x + 5, m E = 4x 15 and m F = 2x Which statement is true? a. DF FE b. E F c. DE FE d. D F 36. In the diagram on the right, which transformation maps GH onto G H? a. Reflection across the y-axis. b. Rotation 180 about the origin. c. Reflection across the x-axis. d. Translation x, y (x + 6, y 8) 37. When writing a proof, which of the following relationships between angles can imply that the angles are congruent? a. Supplementary angles b. Linear pair c. Adjacent angles d. Vertical angles

5 38. In the diagram, AC bisects BAD, and B D. Which criterion can be used to prove ABD ADC? a. SSS c. SAS b. AAA d. AAS 39. Can a triangle have two right angles? Explain. 40. Which of the following can be used to prove that a parallelogram is a rhombus? a. The diagonals are congruent. b. The opposite sides are parallel. c. The diagonals are perpendicular. d. The opposite angles are congruent. 41. Given parallelogram BIRD, find the values of x and y. a. x = 2, y = 10 b. x = 20, y = 2 c. x = 31, y = 111 d. x = 111, y = Which statement is not sufficient to prove that ABCD is a parallelogram? a. AD DC and AB BC b. AC and BD bisect each other c. A C and B D d. AB DC and AB DC 43. Given quadrilateral BIKE, MI = 7x + 2, ME = 6x + 9. What value of x makes BIKE a parallelogram? a. 7 c. 51 b. 14 d Which statement is false? a. A quadrilateral is a square if and only if it is a rhombus and a rectangle. b. A quadrilateral is a rectangle if and only if it has four right angles. c. A parallelogram is a rectangle if and only if its diagonals are congruent. d. A parallelogram is a rhombus if and only if its diagonals are congruent. 45. If quadrilateral WIND is a rectangle, find the length of WN a. 8 c. 24 b. 16 d What is the most specific name for the quadrilateral CATS? a. Rectangle c. Trapezoid b. Parallelogram d. Isosceles trapezoid 47. Which statement about kites is false? a. A kite s diagonals are perpendicular. b. A kite s opposite sides are congruent. c. A kite has two pairs of consecutive congruent sides. d. A kite has exactly one pair of opposite angles that are congruent.

6 48. Find the length of the midsegment of the trapezoid shown. a. 19 c. 21 b. 20 d The diagram of the right shows kite SURF. Find the measure of S. a. 95 c. 160 b. 100 d Which statement about an isosceles trapezoid is false? a. The legs are congruent. b. It has only one pair of congruent base angles. c. Its diagonals are congruent. d. Both pairs of base angles are congruent. 51. Find the value of the variables in the tall parallelogram on the right. a. x = 2, y = 2 c. x = 1, y = 3.2 b. x = 5, y = 2 d. x = 2, y = Find the value of the variables in the parallelogram on the right. a. x = 4, y = 184 c. x = 3, y = 184 b. x = 4, y = 116 d. x = 3, y = Find the value of the variables in the parallelogram. a. n = 4, m = 5 c. n = 5, m = 4 b. n = 6, m = 3 d. n = 2, m = In ABC, AD is a perpendicular bisector of BC. Draw a diagram showing this information and prove that ABC is isosceles. 55. ABCD is a parallelogram with A 2,3 B 5,7 C 3,6. Find point D. a. D(0, 10) b. D( 10, 4) c. D(0.5, 4.5) d. D 8,2 56. The diagonals of rhombus PQRS below intersect at T. Given that m RPS = 30 and RT = 6, find a. m QPR b. m QTP c. RP 57. The diagonals of rectangle WXYZ on the right intersect at P. Given that m YXZ = 50 and XZ = 12, find a. m WXZ b. m WPX c. PY

7 58. Find the value of x. a. b. c. 59. How many angles measuring 58 are there in the diagram on the right? a. 1 b. 2 c. 5 d Use the information in the diagram to find m A, m D, m DNA 61. Nanorta puts up a tent with a crosssection of an isosceles triangle on top of an isosceles trapezoid, as illustrated in the diagram. She measures m A = 62 and m E = 140. Help her figure out m BDE. 62. In the previous question, which of the following properties or theorems is NOT used? a. Vertical angles c. Angle addition postulate. theorem. d. Same side interior angles theorem. b. Triangle sum theorem. 63. Which set of statements is NOT enough to show that AED BEC? a. D C, AE BE, AED BEC b. A B, AE BE, AED BEC c. AE BE, AED BEC, DE CE d. AE BE, AED BEC, AD BC 64. Use the information in the diagram to prove that ABC is isosceles. Follow these steps: a. What is the given information? b. Explain why 2 3. c. Explain why 1 4. d. Show ABD ACE. e. Conclude AB AC. 65. Find KM. 66. Find FE.

8 67. ABCD is a square. E and F are points on BC and DC respectively. Given that BE DF, complete the proof that ABE ADF. 68. For each pair of triangles, determine if they can be proven congruent. If so, identify the congruence criterion that proves they are congruent and write the congruence statement. If not, write inconclusive. a. b. c. ABC by d. e. f. 69. Consider the two triangles in the diagram on the right. a. Can you use the vertical angles theorem to show that AWT PWS? Explain. b. How can you show that WAT WPS? c. Which criterion would you use to prove WAT WPS? d. What kind of triangles are WAT and WPS? What theorem are you relying on? e. Find m AWP. 70. Show that ABCD with A 0,3, B 3,7, C 8,7, D(11,3) is an isosceles trapezoid. 71. Parallelogram ABCD has coordinates A 1,5, B 6,3, C(3, 1). a. Find the coordinates of D. b. What are the coordinates of the point of intersection of the diagonals AC and BD? 72. Complete the proof that opposite angles in a parallelogram are congruent. Given: ABCD Prove: B D

9 Statements ABCD AB CD, BC AD Reasons Given Definition of parallelogram Alternate interior angle theorem Alternate interior angle theorem AC AC ABC B D 73. For each property, specify all quadrilateral that satisfy it. (Write T for trapezoid, IT for isosceles trapezoid, K for kite, P for parallelogram, R for rectangle, D for rhombus/diamond, and S for square) a. The diagonals are congruent. b. Both pairs of opposite sides are congruent. c. Both pairs of opposite sides are parallel. d. All angles are congruent. e. All sides are congruent. f. Diagonals bisect each other. g. Diagonals bisect the angles. h. Diagonals are perpendicular to each other. i. One pair of congruent opposite sides. 74. Which statement is incorrect? a. In an isosceles trapezoid, the diagonals are congruent. b. In an isosceles trapezoid, opposite angles are supplementary. c. In an isosceles trapezoid, a diagonal forms two congruent triangles. d. In an isosceles trapezoid, the diagonals form four small triangles, two of which are congruent. 75. Parallelograms MNOP and OPQR share a side. Prove that MN QR

10 76. Use slopes of sides and diagonals to determine the most specific type of quadrilateral ABCD. a. A 0,3, B 3,0, C 6, 9, D( 9, 6) b. A 0,8, B 3,4, C 3,9, D(0,13) c. A 2,5, B 3, 2, C 8,3, D 6,7 d. A 1,1, B 4,5, C 9, 7, D(6, 11) 77. Complete the flowchart proof. Given: RHOM is a rhombus, OB RM, RU MO. Prove: OB RU 78. Quadrilateral ABCD is a rhombus. a. If m BAE = 32, find m ECD. b. If m EDC = 43, find m CBA c. If m EAB = 57, find m ADC d. Find x given that m BEC = 3x 15. e. Find x given that m ADE = 5x 8 and m CBE = 3x + 24

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