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1 1 st Semester Final xam Review Name: Geometry ate: lock: You must show your work to receive full credit! Write your final answer on the blank provided. Topic #1 (Foundations of Geometry) 1) Multiple hoice: The notation for the length of the segment between P and Q is?. a. PQ b. PQ c. PQ d. PQ 2) Multiple hoice: Which of the following is a correct name for a plane? a. W b. WX c. WXY d. WXYZ 3) Multiple hoice: Which of the following is a correct name for a line? a. L b. LI c. LIN d. LIN 4) efine collinear. 5) Let be between and. If = 3v 30, = 6v 15, and = 27, use the v = Segment ddition Postulate to solve for v. (Hint: raw a diagram and label the given information!) 6) If m IOJ = 22 and m HOI = 25, then what is m HOJ? m HOJ = H I O J 7) The m JHI = (2x + 7), m GHI = (8x 2), and m JHG = 65. m JHI = Find m JHI and m GHI. m GHI = I J G H
2 8) What is the midpoint of a segment with endpoints ( 8, 8) and (7, 8)? 9) Find the length of a segment with endpoints ( 4, 7) and ( 6, 4). 10) Multiple hoice: If ROS is obtuse and TOR is straight, then TOS is what kind of angle? S T O R a. cute b. Right c. Obtuse d. Straight 11) Multiple hoice: Which does not name the angle below? a. b. c. d. 12) In the figure (not drawn to scale), MO bisects LMN, m LMO = (13x 31), x = and m NMO = (x + 53). Solve for x and find m LMN. m LMN = L O N M 13) If m JOK = 28 and m JOL = 58, then what is m KOL? m KOL = J K O L
3 14) The measure of an angle is 98. lassify that angle as acute, right, obtuse, or straight. 15) The measure of an angle is 179. lassify that angle as acute, right, obtuse, or straight. 16) Multiple hoice: Name an angle adjacent to O. O a. O b. O c. O d. O 17) True or False: In the figure shown, m = 108, Is m = 72? 18) Solve for x. x = (4x+90) (2x+72) 19) efine supplementary angles. 20) efine complementary angles. 21) Name a pair of vertical angles in the figure below ) Write the converse of the following: If it is raining, then I should use an umbrella.
4 Topic #2 (Parallel and Perpendicular Lines) 23) efine coplanar. 24) Multiple hoice: In the figure shown below, and HG are?. F G H a. Parallel b. Skew c. ongruent d. Perpendicular 25) Name a plane that is parallel to plane F. F G H 26) Multiple hoice: In the figure below, 6 and 3 are? a. lternate xterior b. Same-Side Interior c. lternate Interior d. orresponding 27) Multiple hoice: In the figure below, 6 and 2 are? a. lternate xterior b. Same-Side Interior c. lternate Interior d. orresponding
5 28) If PQ RS, find m 1. m 1 = P 75 Q R 1 S 29) Multiple hoice: In the figure below, H G and m = 100. Which of the following statements is false? a. m = 80 b. m F = 80 c. and are corresponding angles d. and G are alternate interior angles F H G 30) Use the figure below to find m 6. m 6 = ) Use the figure below to find m 4. m 4 = ) What is the slope of a line perpendicular to y = 7x + 13? 33) What is the slope of a line parallel to y = 6x 1? 34) Find the slope of the line between (5, 2) and ( 13, 6)
6 35) Write an equation of a line in slope intercept form that passes through (1, 4) and is: a. Parallel to y = 1 x 4 3 b. Perpendicular to y = 1 x ) Find the value of x. x = (2x) (x 10) 55 37) Find the value of x. x = 31 (x 15) 38) Find the value of x. x = x x ) Find the value of x. x = x 48 21
7 Topic #3 (Transformations) 40) Multiple hoice: Which of the following shows a triangle and its image transformed by R x axis? a. b. c. d. 41) Give the coordinates of the points after the following transformation: R (270,(0,0)) ( 2, 7) (, ) (0, 1) (, ) (3, 8) (, ) 42) Give the coordinates of the points after the following transformation: r (90,(0,0)) ( 2, 7) (, ) (0, 1) (, ) (3, 8) (, ) 43) Give the coordinates of the points after the following transformation: r (180,(0,0)) ( 2, 7) (, ) (0, 1) (, ) (3, 8) (, ) 44) Give the coordinates of the points after the following transformation: T <2, 6> ( 2, 7) (, ) (0, 1) (, ) (3, 8) (, ) 45) Give the coordinates of the points after a dilation with a scale factor n = 2.5 ( 2, 7) (, ) (0, 1) (, ) (3, 8) (, ) 46) Multiple hoice: escribe in words the transformation represented by the following composition: r T XYZ (90,(0,0)) 4,2 a. Translation left 4, up 2 followed by a rotation of 90 clockwise about the origin b. Rotation of 90 clockwise about the origin followed by a translation left 4, up 2 c. Translation left 4, up 2 followed by a rotation of 90 counterclockwise about the origin d. Rotation of 90 counterclockwise about the origin followed by a translation left 4, up 2 47) Multiple hoice: escribe in words the translation represented by T <6, 3> a. 3 units to the left, 6 units up b. 6 units to the left, 3 units up c. 3 units to the right, 6 units down d. 6 units to the right, 3 units down
8 Topics #4 5 (Triangles) 48) escribe a congruence transformation that maps YF to PVG. 49) Multiple hoice: If MNO VWX, which statement is NOT true? a. NO VW b. MO VX c. O X d. N W 50) Given LMN UVW, complete the statements to the right. UW VWU 51) Identify the congruence postulate/theorem that proves the triangles congruent (SSS, SS, S, S, or HL). Then, complete the congruence JHZ statement. V H Z J 52) Multiple hoice: What must be true in order for by SS? a. b. c. d.
9 53) Multiple hoice: Refer to the figure below. Which of the following statements is true? U T V W a. TUV XWV by S b. TUV VWX by SS c. TUV WXV by SS d. TUV XVW by SSS X 54) State the two congruence postulates/theorems (SSS, SS, S, S, or HL) that can be used to prove that O O. O 55) Name the congruence postulate/theorem (SSS, SS, S, S, or HL) that proves. 56) Identify the congruence postulate/theorem that proves the triangles congruent (SSS, SS, S, S, or HL). Then, complete the congruence NMO statement. N R O M P
10 57) In the diagram below, is the perpendicular bisector of. If = 36, find the value of x,,, and. 15 x = = = = 3x 18 58) Find the measure of each base angle in the isosceles triangle below ) Find the value of x in the isosceles triangle below. x = x 30 60) Multiple hoice: Which of the following could be sides of a triangle? a. 15 cm, 4 cm, 20 cm b. 3 cm, 15 cm, 20 cm c. 11 cm, 5 cm, 16 cm d. 5 cm, 12 cm, 16 cm 61) In, = 9, = 10, and = 11. Identify the largest angle of.
11 Topic #6 (Quadrilaterals) 62) Name the figure shown below. 63) omplete the table below naming each polygon based on the number of sides. # of Type of Polygon Sides ) Three angles of a quadrilateral are 113, 66, and 67. What is the measure of the missing angle. 65) Find the values of x and y. x = y = 126 y 65 x ) Find the values of x and y. x = y = y 114 x ) In parallelogram LMNO, ON = 7x 5, LM = 6x + 3, NM = x 4, x = and OL = 2y + 5, find the values of x and y. y =
12 68) In the parallelogram below, T = 6x - 7 and TG = 23. Find the value of x. L G T V 69) Find the value of x in the parallelogram below. 97 (11x 5) 70) Find the values of x and y in the parallelogram below. (4y) (3x 18) (2x+12) (5x 42) 71) ecide if you can prove if each figure is a parallelogram. Justify your answer. a. b. c. d.
7. m JHI = ( ) and m GHI = ( ) and m JHG = 65. Find m JHI and m GHI.
1. Name three points in the diagram that are not collinear. 2. If RS = 44 and QS = 68, find QR. 3. R, S, and T are collinear. S is between R and T. RS = 2w + 1, ST = w 1, and RT = 18. Use the Segment Addition
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