Name: Extra Midterm Review January 2018

Transcription

1 Name: Extra Midterm Review January Which drawing best illustrates the construction of an equilateral triangle? A) B) C) D) 2. Construct an equilateral triangle in which A is one vertex. A 3. Construct an equilateral triangle inscribed in circle T shown below. [Leave all construction marks.]

2 4. As shown in the diagram below of, a compass is used to find points D and E, equidistant from point A. Next, the compass is used to find point F, equidistant from points D and E. Finally, a straightedge is used to draw. Then, point G, the intersection of and side of, is labeled. 6. Base your answer to the following question on On the diagram below, use a compass and straightedge to construct the bisector of. Which statement must be true? A) bisect side B) bisects BAC C) D) ABG ACG 5. Using a compass and straightedge, construct the bisector of. [Leave all construction marks.] 7. Which diagram shows the construction of the perpendicular bisector of? A) B) C) D)

3 8. Based on the construction below, which conclusion is not always true? Extra Midterm Review A) B) AB = CD C) AE = EB D) CE = DE 9. Base your answer to the following question on Using a compass and straightedge, construct a line perpendicular to through point P. [Leave all construction marks.]

4 10. On the answer sheet, construct a line through P perpendicular to. 13. In shown below, L is the midpoint of, M is the midpoint of, and N is the midpoint of. 11. Construct the perpendicular bisector of side. If,, and, the perimeter of trapezoid BMNC is A) 26 B) 28 C) 30 D) In the accompanying diagram, line a intersects line b. 12. In the diagram below of,,, and. What is the value of x? A) 10 B) 5 C) 10 D) In the accompanying diagram, lines and intersect at N, m JNL = 6x - 74, and m MNK = 2x What is the value of x? Point P must be the A) centroid B) circumcenter C) incenter D) orthocenter

5 16. In the diagram below, and are shown with m and. 19. In the accompanying diagram,,, and m 1 = 105. What is m 2? What is m? A) 125 B) 115 C) 65 D) Base your answer to the following question on The pentagon in the diagram below is formed by the five rays. 20. In the accompanying diagram, is parallel to, m DBA = 40, and m BCE = 105. Which statement is true? A) is the longest side of ABC. B) is the longest side of ABC. C) ABC is an isosceles triangle. D) ABC is an obtuse triangle. 21. In the accompanying diagram, ABCD is a rhombus and m EAD = 110. Find m CBF. What is the degree measure of angle x? A) 72 B) 96 C) 108 D) In the accompanying diagram, is parallel to and both lines are intersected by transversal m BEF is twice m DFE, find m DFE.. If

6 22. In the accompanying figure, two parallel lines and are cut by transversal intersecting in G and in H. If m BGH = (2x + l0) and m GHD = (3x - 20), find the value of x. 23. In the accompanying diagram,,,, and are straight lines. If m w = 30, m x = 30, and m z = 120, find m y. 24. In the accompanying diagram, is extended to C, m DBC = 142, and. Find m EAB.

7 25. Which statement is illustrated in the construction sketched below? 27. Base your answer to the following question on As shown in the diagram below, lines m and n are cut by transversal p. A) Through a point not on a given line, exactly one line can be drawn perpendicular to the given line B) If two lines cut by a transversal form congruent alternate interior angles, then the two lines are parallel. C) If two lines cut by a transversal form congruent corresponding angles, then the two lines are parallel. D) If two lines cut by a transversal form same side interior angles that are supplementary, then the two lines are parallel. 26. Transversal intersects and, as shown in the diagram below. If m l = 4x + 14 and m 2 = 8x + 10, lines m and n are parallel when x equals A) 1 B) 6 C) 13 D) In the accompanying diagram of ABC,,, m BDA = 70, and m EDC = 40. What is m DAC? 29. In the accompanying diagram,,, BCD is an exterior angle formed by extending to point D, and. Find the value of x. Which statement could always be used to prove? A) B) C) and are supplementary D) and are supplementary

8 30. In the accompanying diagram, ACD is an exterior angle of ABC. If m B = 40, m A = 2x, and m ACD = 3x, what is the value of x? 35. In the diagram below of Isosceles, the measure of vertex angle B is 80. If extends to point D, what is? A) 35 B) 30 C) 35 D) In a triangle, one exterior angle measures 36º. What is the probability that the triangle is a right triangle? A) 1 B) C) D) In ABC, m A is three times m B. An exterior angle at vertex C measures 100. What is m B? 33. In the accompanying diagram, is the bisector of ACB, m A = 58, and m B = 72. Find m ACD. 34. In the accompanying diagram of ABC, m B = 80. A) 50 B) 80 C) 100 D) If the measures of the three angles of a triangle are represented by x, 2x 20, and 3x 10, then the triangle is A) right B) obtuse C) isosceles D) equilateral 37. Side of PQR is extended through Q to point T. Which statement is not always true? A) m RQT > m R B) m RQT > m P C) m RQT = m P + m R D) m RQT > m PQR 38. Find the image of the point (6, 2) under the rotation R90º about the origin. 39. If the coordinates of point P are ( 5,9), then (R30º R75º) is equivalent to A) (R20º R25º)(P) B) (R 20º R75º)(P) C) (R90º R90º)(P) D) (R60º R15º)(P) What is the value of? A) 40 B) 50 C) 100 D) 140

9 40. As shown in the graph below, the quadrilateral is a rectangle. Extra Midterm Review Which transformation would not map the rectangle onto itself? A) a reflection over the x-axis B) a reflection over the line x = 4 C) a rotation of 180 about the origin D) a rotation of 180 about the point (4,0) 41. Which rotation about its center will carry a regular decagon onto itself? A) 54 B) 162 C) 198 D) Which regular polygon has a minimum rotation of to carry the polygon onto itself? A) octagon B) decagon C) hexagon D) pentagon 43. What are the coordinates of P', the image of P(1,2) after a reflection in the origin? 44. What is the image of (6, 1) after a reflection in the x axis?

10 45. Triangle SUN has coordinates S(0,6), U(3,5), and N(3,0). On the accompanying grid, draw and label SUN. Then, graph and state the coordinates of S'U'N', the image of SUN after a reflection in the y-axis. 46. A translation maps A(2,6) to A(5,4). Find the coordinates of the image of ( 1,2) under the same translation. 47. A translation maps P(3, 2) onto P'(5,0). Find the coordinates of the image of Q(4, 6) under the same translation. 48. Main Street and Park Avenue intersect at an angle of 74º. Mr. Jones lives on Main Street, 50 meters from the intersection, and Mr. Smith lives on Park Avenue, 40 meters from the intersection. The triangle formed by the intersection and the houses is an acute triangle. Find, to the nearest meter, the distance between Mr. Jones' house and Mr. Smith's house. 49. Pentagon PQRST has parallel to. After a translation of T2, 5, which line segment is parallel to ' '? A) ' ' B) ' ' C) ' ' D) ' ' 50. Translation T maps point (2,6) to point (4, 1). What is the image of point ( 1,3) under translation T? 51. The graph of y = (x 3) 2 is shifted left 4 units and down 2 units. What is the axis of symmetry of the transformed graph? A) x = 2 B) x = 1 C) x = 1 D) x = A transformation maps P(x,y) onto P'(x 2,y+3). Under the same transformation find the coordinates of Q', the image of Q( 4,1).

11 53. A transformation maps P(x,y) onto P'(x + 3, y 2). Find the coordinates of Q, whose image under the same transformation is Q'(6,2). 54. What are the coordinates of the image of point under the translation? A) B) C) D) 55. Find the coordinates of P', the image of P( 3,4) under the translation T4, Which transformation would result in the perimeter of a triangle being different from the perimeter of its image? A) B) C) D) 57. After a composition of transformations, the coordinates A(4,2), B(4,6), and C(2,6) become A" ( 2, 1), B"( 2, 3), and C"( 1, 3), as shown on the set of axes below. 58. When ABC is dilated by a scale factor of 2, its image is A'B'C'. Which statement is true? A) ' ' B) A A' C) perimeter of ABC = perimeter of A'B'C' D) 2(area of ABC) = area of A'B'C' 59. Quadrilateral undergoes a transformation, producing quadrilateral. For which transformation would the area of not be equal to the area of? A) a rotation of about the origin B) a reflection over the y-axis C) a dilation by a scale factor of 2 D) a translation defined by 60. Which transformation would not always produce an image that would be congruent to the original figure? A) translation B) dilation C) rotation D) reflection Which composition of transformations was used? A) B) C) D)

12 61. The coordinates of, shown on the graph below, are Graph and label, the image of after it is reflected over the y-axis. Graph and label, the image of after it is reflected over the x-axis. State a single transformation that will map onto.

13 62. The coordinates of the vertices of are A( 6, 5), B( 4, 8), and C(1, 6). State and label the coordinates of the vertices of, the image of after the composition of transformations. 63. The coordinates of the endpoints of are A(-2,4) and B(4,1). a On a set of axes, graph. b On the same set of axes, graph and state the coordinates of (1) ' ' the image of after a reflection in the x axis (2) '' '' the image of ' ' after a translationthat shifts (x,y) to (x + 2,y) c Using coordinate geometry, determine if ' ' = '' '' Justify your answer.

14 64. In the accompanying figure, lines and m are lines of symmetry. What is rm r ( )? 67. In the accompanying diagram, line s is parallel to line t. Which is equivalent to the composition of line reflections ( ABC)? A) B) C) D) 65. In the accompanying diagram, p and q are symmetry lines for rectangle ABCD. Find rp rq rp(a). A) a rotation B) a line reflection C) a translation D) a glide reflection 68. Given ABC with points A(4,3), B(4, 2), and C (2,3). (1) On graph paper, sketch ABC. (2) On the same set of axes, graph and state the coordinates of A'B'C', the image of ABC after a reflection in the line y = x. (3) On the same set of axes, graph and state the coordinates of A"B"C", the image of A'B'C' after the translation T 4, Triangle ABC had coordinates A(-3,-7), B(-3,-3), and C(0,-3). a On graph paper, graph and label ABC. b Graph and state the coordinates of A'B'C', the image of ABC after a point reflection in the origin. c Graph and state the coordinates of A''B''C'', the image of A'B'C' reflected in the line y = 2. d Graph and state the coordinates of A'''B'''C''', the image of A''B''C'' after translation T(8,2).

15 69. As graphed on the set of axes below, is the image of after a sequence of transformations. Is congruent to? Use the properties of rigid motion to explain your answer. 70. If, which graph represents f(x) under the composition? 71. Which statement is not always true when? A) B) C) D) 72. Base your answer to the following question on In the diagram below, Which two statements identify corresponding congruent parts for these triangles? A) and C Y B) and C X C) and A Y D) and A X

16 73. In the diagram of ABC and DEF below,, A D, and B E. Which method can be used to prove ABC DEF? A) SSS B) SAS C) ASA D) HL 74. In the diagram below, four pairs of triangles are shown. Congruent corresponding parts are labeled in each pair. 75. The diagram below shows the construction of the bisector of ABC. Which reason for triangle congruence is used in proving that bisects ABC? A) ASA B) SAS C) SSS D) SAA 76. In the diagram of trapezoid ABCD below, diagonals and intersect at E and ABC DCB. Using only the information given in the diagrams, which pair of triangles can not be proven congruent? A) A B) B C) C D) D Which statement is true based on the given information A) B) C) CDE BAD D) CDB BAC

17 77. In the accompanying diagram of quadrilateral ABCD, diagonal bisects BAD and BCD. 81. In parallelogram ABCD, the measure of ABC is 130. Find the measure, in degrees, of DAB. Which statement can be used to prove that ABC ADC? A) HL HL B) SSS SSS C) ASA ASA D) SAS SAS 78. If ABC JKL RST,then must be congruent to A) B) C) D) 79. In the diagram below, bisects at B, and bisects at C. 82. In quadrilateral ABCD, if and, then diagonals and must A) be perpendicular B) be parallel C) be congruent D) bisect each other 83. Which statement is not true for all parallelograms? A) Opposite sides are parallel. B) Opposite sides are congruent. C) The diagonals bisect each other. D) The diagonals are congruent. 84. If quadrilateral ABCD is a parallelogram, which statement must be true? Which statement is always true? A) B) C) D) 80. Which statement is not valid for proving that two triangles are congruent? A) SAS SAS B) SSA SSA C) ASA ASA D) AAS AAS A) B) C) bisects DAB and BCD. D) and bisect each other. 85. In parallelogram ABCD, diagonals and intersect at E. Which statement is always true? A) Triangle AED is isosceles. B) Triangle ABD is a right triangle. C) Triangle AEB is congruent to triangle AED. D) Triangle ABC is congruent to triangle CDA. 86. Given these distinct quadrilaterals: parallelogram, rhombus, rectangle, square, and isosceles trapezoid. What is the probability of choosing at random a quadrilateral whose diagonals are always congruent?

18 87. In parallelogram ABCD, diagonals and intersect at E. Which statement is always true? A) Triangle AED is isosceles. B) Triangle ABD is a right triangle. C) Triangle AEB is congruent to triangle AED. D) Triangle ABC is congruent to triangle CDA. 88. In the diagram below, ABCD is a parallelogram, is extended through B to E, and is drawn. Extra Midterm Review if and, what is? A) B) C) D) 89. In the diagram below of rectangle RSTU, diagonals and intersect at O. If and, what is the length of? A) 8 B) 2 C) 16 D) In parallelogram ABCD, diagonals and intersect at E. If BE = 4x 12 and DE = 2x + 8, find x. 91. The corresponding medians of two similar triangles are 8 and 20. If the perimeter of the larger triangle is 45, what is the perimeter of the smaller triangle? A) 14 B) 18 C) 33 D) 37

19 92. In the diagram below, is a median of triangle PQR and point C is the centroid of triangle PQR. If and, determine and state the length of. 93. As shown below, the medians of intersect at D. 97. Quadrilateral ABCD is graphed on the set of axes below. If the length of is 12, what is the length of? A) 8 B) 9 C) 3 D) The diagonals of a rhombus have lengths of 16 and 30. The length of a side of the rhombus is A) 17 B) 15 C) 16 D) Which type of quadrilateral has diagonals that will always divide it into four congruent triangles? A) rhombus B) rectangle C) trapezoid D) isosceles trapezoid 96. Find the length of a side of the rhombus whose diagonals measure 12 and 16. Which quadrilateral best classifies ABCD? A) trapezoid B) rectangle C) rhombus D) square 98. In rhombus ABCD, AB = 2x 2 and BC = x + 8. Find the length of. 99. In rectangle ABCD with diagonals and, AC = 3x 15 and BD = 7x 55. Find x.

20 100. Which of the following statements is false? A) All squares are parallelograms. B) All squares are rectangles. C) All rectangles are squares. D) All rectangles are parallelograms In rectangle ABCD, AC = 2x + 15 and BD = 4x 5. Find x Which statement is always true? A) A quadrilateral is a trapezoid. B) A rhombus is a square. C) A trapezoid is a parallelogram. D) A rectangle is a parallelogram Which quadrilateral must have congruent diagonals? A) trapezoid B) rectangles C) rhombus D) parallelogram 104. Which statement is true? A) Every square is a rhombus. B) Every rhombus is a square. C) Every trapezoid is a parallelogram. D) Every parallelogram is a rectangle Which statement is always true? A) A square is a rhombus. B) A parallelogram is a square. C) A rhombus is a rectangle. D) A rectangle is a rhombus Which polygon must have congruent diagonals? A) rhombus B) square C) parallelogram D) trapezoid 107. Quadrilateral MNOP is a trapezoid with. If M'N'O'P' is the image of MNOP after a reflection over the x-axis, which two sides of quadrilateral M'N'O'P' are parallel? A) B) C) D) 108. A set contains 5 quadrilaterals: a rectangle, a rhombus, a parallelogram, a square, and an isosceles trapezoid. If one quadrilateral is selected from the set at random, what is the probability that its diagonals bisect each other? 109. A quadrilateral whose diagonals bisect each other and are perpendicular is a A) rhombus B) rectangle C) trapezoid D) parallelogram 110. Base your answer to the following question on In the diagram below of ABC, medians,, and intersect at G. If CF = 24, what is the length of? A) 8 B) 10 C) 12 D) Base your answer to the following question on In the diagram below of ACT, D is the midpoint of, O is the midpoint of, and G is the midpoint of. If AC = 10, AT = 18, and CT = 22, what is the perimeter of parallelogram CDOG? A) 21 B) 25 C) 32 D) 40

21 112. In the diagram below, ~ Base your answer to the following question on As shown in the diagram below, ABC DEF, AB = 7x, BC = 4, DE = 7, and EF = x. If,,, and the perimeter of is 30, what is the perimeter of? A) 12.5 B) 14.0 C) 14.8 D) In the diagram of below,,,, and. What is the length of? A) 28 B) 2 C) 14 D) In shown below, medians intersect at point R. What is the length of, to the nearest tenth? A) 5.1 B) 5.2 C) 14.3 D) 14.4 If, what is the value of x? A) 9 B) 12 C) 15 D) 27

22 116. Triangle RST is similar to with RS = 3 inches and XY = 2 inches. If the area of is 27 square inches, determine and state the area of, in square inches In, D is the midpoint of and E is the midpoint of. If AC =3x 15 and DE = 6, what is the value of x? 119. In the diagram below of, A) 6 B) 7 C) 9 D) In the diagram below, Which measurements are justified by this similarity? A) AD = 3, AB = 6, AE = 4, and AC = 12 B) AD = 5, AB = 8, AE = 7, and AC = 10 C) AD = 3, AB = 9, AE = 5, and AC = 10 D) AD = 2, AB = 6, AE = 5, and AC = 15 If,,, and, what is the length of? A) 10 B) 8 C) 6 D) In ABC and DEF, =. Which additional information would prove ABC DEF? A) AC = DF B) CB = FE C) ACB DFE D) BAC EDF 121. If two angles of one triangle are congruent, respectively, to two angles of another triangle, then these triangles must be A) isosceles B) similar C) congruent D) equilateral 122. In the diagram below,. If similarly by SAS? A) B) C) D), which statement will justify

23 123. If, which statement is not always true? A) B) C) D) 124. In the diagram below of, Q is a point on, S is a point on, is drawn, and Base your answer to the following question on In the diagram of ABC and EDC below, and intersect at C, and CAB CED. Which method can be used to show that ABC must be similar to EDC? A) SAS B) AA C) SSS D) HL Which reason justifies the conclusion that PRT SRQ? A) AA B) ASA C) SAS D) SSS 125. The image of after a dilation of scale factor k centered at point A is, as shown in the diagram below. Which statement is always true? A) B) C) D)

24 127. In right triangle ABC shown below, altitude is drawn to hypotenuse. Prove ABC ~ ACD In the diagram below of circle O, tangent is drawn to diameter. Chord is parallel to secant, and chord is drawn. Prove : 129. In the diagram below, is parallel to, and intersects at A. Prove: GA x TN = TA x GI

25 Answer Key Midterm Review 1. B 2. construction 3. A correct construction is drawn showing all appropriate arcs. 4. B 5. drawn shown appropriate arcs, and the angle bisector is drawn. 6. A correct construction is drawn showing all appropriate arcs, and the angle bisector is drawn. 7. A 8. B 9. A correct construction is drawn showing all appropriate arcs Construction 12. A 13. D 14. C B 17. C A C 26. C 27. C D 31. D B 35. D 36. B 37. D 38. (2,6) 39. D 40. C 41. D 42. A 43. ( 1, 2) 44. (6,1) 45. S'(0,6), U'( 3,5), N' ( 3,0) 46. (2,0) 47. (6, 4) C 50. (1, 4) 51. B 52. ( 6,4) 53. (3,4) 54. A 55. (1,5) 56. C 57. C 58. B 59. C 60. B 61. are graphed and labeled correctly and a rotation of or a reflection through the origin is stated. 62. A" (10, 0), B" (8, 3), C" (3, 1) 63. b (1) A'( 2,- 4), B' (4, 1) (2) A''(0, 4), B'' (6, 1) 64. C 65. D 66. b A'(3,7), B'(3,3), C'(0,3) c A''(3,3), B''(3,1), C''(0,1) d A'''(5,1), B'''(5,3), C'''(8,3) 67. C 68. (2) A'(3,4), B'( 2,4), C'(3,2) (3) A''( 1,7), B'' ( 6,7), C''( 1, 5) 69. Yes B 72. D 73. C 74. A 75. C 76. D 77. C 78. C 79. A 80. B D 83. D 84. D 85. D D 88. A 89. C B A 94. A 95. A C C D 103. B 104. A 105. A 106. B 107. A A 110. A 111. C 112. D 113. C 114. C 115. A C 118. D 119. C

26 Answer Key Midterm Review 120. C 121. B 122. A 123. A 124. A 125. D 126. B 127. A complete and correct explanation is written Correct proofs are written A complete and correct proof that includes a conclusion is written.