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Name_____________________________________________Date_______________________Period________________ 1st Semester Geometry Final Review (1) Write a vector describing the translation seen on this set of axes? (3) If x = 3, list the angles from smallest to largest. (2) Write a vector describing the following translation: (4) If x = 4 name the smallest angle. (Picture not drawn to scale.) A 3x - 2 2x - 3 x-2 x+3 C B 15 -x 2x + 2 (5) What is the intersection of plane STXW and plane SVUT? a. SV b. ST c. YZ d. TX (6) What is the intersection of plane ABCD and plane CDEF? a. CD b. AC c. EC d. EA (7) If triangle ABC is reflected across the x- axis, what would be the coordinate of B’? (9) Classify the following triangle by its angles and its sides. (Picture not drawn to scale.) 36° 6x – 20 + 2x + 36 = 180 6x + 20 = 2x + 36 6x -20 = 90 6x – 20 = 2x + 36 (10) Classify the following triangles by its angles and its sides. 108° (11) Given MO bisects angle < LMN. m < LMO = 6x - 20, and m< NMO = 2x + 36. Which of the following equations is used to find the value of x? a. b. c. d. (8) If the following image is reflected over x-axis, what are the coordinates of the final image: (12) Given BC bisects <ABD. Which equation can be used to solve for the value of x? a. 2X-10 = x+70 b. 2X-10 + x+70 = 180 c. 3x – 60 d. 2X-10 + X+70 = 90 (13) What would be the coordinates of A’B’C’ if the following triangle were dilated by a scale factor of 2? (14) Which of the following statements is true about the dilation of the image? (a) All corresponding angles increased by a scale factor of 2 (b) All corresponding angles increased by a scale factor of ½ (c) All corresponding sides increased by a scale factor of 2 (d) All corresponding sides increased by a scale factor of ½ (15) What type of segment is BD? (16) Describe the following special segments: a) Altitude – _______________________________ _______________________________________ _______________________________________ b) Median - ________________________________ ________________________________________ ________________________________________ c) Perpendicular Bisector-_____________________ ________________________________________ ________________________________________ (17) A plane takes off from a base at (8, 7) on a coordinate grid. The pilot gets halfway to his destination when he realizes he has to refuel. His halfway point is at (7,5). What point is closest to his destination ? (18) A boy leaves his house at 4,5 on a coordinate grid. When he gets halfway to school he realized he forgot his homework. His halfway point is at (1, 3). At which point is his school located? a. (3, 6) b. (3, 13) c. (6, 3) d. (6, 13) a. (0,0) b. (-2, 1) c. (1, -2) d. (7, 7) (19) Describe this transformation: (20) Which of the following statements would describe the transformation shown in the picture: (a) (b) (c) (d) A 45° rotation about the origin A 90° rotation about the origin A reflection across y = -1/2x A translation (21) Find the value of angle R If angle S = 72° (22) Write an equation to find the value of X if S (3x 4)° and U (3x 4)° and T ( x 2)° (23) A geometry student concluded that: (24) Draw a counterexample for the following conclusion: If 2 sides and a non-included angle of one triangle are congruent to 2 sides and a non-included angle of another triangle, then the triangles are congruent. If all of the angles in one triangle are congruent to all of the angles in another triangle, then the triangles are congruent. Which diagram could be used as a counterexample to his conclusion? A. C. B. D (25) AF bisects CAB. If CAB= 78˚, FAB = 5x + 3 and find x. (26) In the diagram below, YT bisects WYZ . If the m3 108 and m 2 = 2x + 4 then what is the m2 and m1? W 3 X Y T 2 1 Z (27) Find the value of x. (28) Find the value of x. (29) Rico’s home is at coordinates (-2, 4). He decides to meet his friend Paul at a coffee shop that is at coordinates (5, 8). The coffee shop is at the midpoint between Rico’s and Paul’s homes. What are the coordinates of Paul’s home? (30) What is the midpoint of (4,4) and (-2, -7)? (31) Which of the following could not be the 3rd side if 2 side lengths of the triangle were 3 and 10? A. 11 B. 7.2 C. 6 D. 12.3 (32) Which of the following could not be the 3rd side if 2 side lengths of the triangle were 18 and 12? A. 11.3 B. 6.2 C. 29.9 D. 5.4 (33) Determine the intersection of the 2 planes: (34) Find the intersection of planes D and H D D (35) Which congruency postulate proves the triangles congruent? A. B. C. D. E. SSS SAS AAS ASA Not Congruent (37) Which congruency postulate proves the triangles congruent? A. SSS B. SAS C. AAS D. ASA E. Not Congruent (39) Which statement must be true if you want to use the given shortcut to prove the triangles congruent? A. B. C. D. <D = <A <B = <C AB = CD AM = DM (36) Which congruency postulate proves the triangles congruent? A. SSS B. SAS C. AAS D. ASA E. Not Congruent (38) Which congruency postulate proves the triangles congruent? A. B. C. D. E. SSS SAS AAS ASA Not Congruent (40) Which statement must be true if you want to use the given shortcut to prove the triangles congruent? A. B. C. D. <Z = <W <ZYX = <WYX XZ = XW WY = ZY (41) Fill in the reasons for the following proof. Given: M is the midpoint of BY AM = MZ Prove: ∆ABM = ∆ZYM Statements M is the midpoint of BY BM = YM <B = <Y AB = XY ∆ABM = ∆XYM Reasons Given Definition of midpoint Definition of ________ _____________ Given ________ congruency postulate (42) Fill in the reasons for the following proof. Given: <B = <D C is the midpoint of BD Prove: ∆ABC = ∆EDC Statements C is the midpoint of BD BM = YM <ACB = <ECD <B=<D ∆ABM = ∆XYM (43) Solve for X. (44) Solve for X. (45) Find X. (46) Find X. Reasons Given Definition of midpoint Definition of ________ _____________ Given ________ congruency postulate