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Grade 8 Geometry Review 1.(8G1a) Which sequence of transformations takes A B C D A to its image, B ? reflection over the x-axis and translation 2 units down reflection over the y-axis and translation 2 units down translation 2 units down and 900 rotation a b o u t the origin translation 12 units right and 900 rotation a b o u t the origin 2. (8G5) In the diagram below, rays g and h are parallel. Triangle JKL has vertices J and L on ray g and vertex K on ray h. The sum of the measures of 1 and 2 is 1520 What is the measure, in degrees, of A 28 B 38 3? C 62 D 208 3. (8G4) Rectangle R undergoes a dilation with scale factor 0.5 and then a reflection over the y-axis. The resulting image is Rectangle S . Which statement about Rectangles R and S is true? A They are congruent and similar. C They are congruent but not similar. B They are similar but not congruent. D They are neither congruent nor similar. 4. (8G3) Vertex J of rectangle FGHJ is located at (4, 2). A dilation of FGHJ will result in the image F'G'H'J'. If the dilation is centered at the origin and has a scale factor of 2, what are the coordinates of J'? A (8,4) B (7,6) C (4,2) D (2,1) 5. (8G1a) Giselle will transform ∆XYZ shown below, using only rotations, reflections, and translations. The vertices of ∆XYZ have integer coordinates. What is the length of the image of XY after Giselle transforms the figure? A any length less than 4 units C any length greater than 4 units B exactly 4 units D any length 6. (8G4) The image of ∆ABC after two transformations is ∆A’B’C’, as shown on the coordinate grid below. Which sequence best describes these two transformations? A dilation and then translation B dilation and then reflection C reflection and then rotation D translation and then rotation 7.(8G5) In the figure below, lines a and b are parallel and line c is a transversal. Which statement explains why A B C D 2 is congruent to 6 The angles form a straight line. The angles are on opposite sides of the transversal. The angles have measures that sum to a straight angle. The angles have the same relative positions on the transversal. 8.(7G5) In the diagram of ∆RST below, S measures 54° and form an exterior angle of 115°, T measures x0. Side SR is extended to What is the value of x, in degrees? A 36 B 61 C 115 9. (8G3) The rectangle shown below is to be reflected over the y-axis. Which statement about the resulting image will be true? A B C D All All All All x coordinates and y coordinates are positive. x coordinates and y coordinates are negative. x coordinates are positive and all y coordinates are negative. x coordinates are negative and all y coordinates are positive. D 126 1 0 .(8G9) A water tank is in the shape of a right circular cylinder with a height of 20 feet and a volume of 32π cubic feet. What is the diameter, in feet, of the water tank? A 16 B 10 C 8 D 4 11.(8G3) If ∆ABC is rotated 900 clockwise about the origin, what will be the new coordinates of vertex B? I A (-1, -4) B (1, 4) C (4, 1) D (4, -1) 12.(8G9) A spherical ball has a radius of 4 inches. What is the volume, in cubic inches, of the ball in terms of π? A 64π 3 B 48π C 64π D 256π 3 13.(8G1b) Quadrilateral PQRS will be rotated 200 clockwise about point Q. What is the measure of A 200 PQR as a result of this rotation? B 570 C 770 D 970 14.(8G2) Triangle ABC was rotated 900 clockwise. Then it underwent a dilation centered at the origin with a scale factor of 4. Triangle A'B'C' is the resulting image. What parts of ∆A'B'C' are congruent to the corresponding parts of the original triangle? Explain your reasoning. _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ Compare the perimeters of ∆ABC and ∆A'B'C'. Explain your reasoning. ___________________________________________________________________________________ ___________________________________________________________________________________ ___________________________________________________________________________________ 15. (8G3) Pentagon D, on the coordinate plane below, is the image of pentagon C after a sequence of transformations. Describe a sequence of transformations that will take pentagon C to its image, pentagon D _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ 16. (8G9) Mr. Tarpey wanted his students to compare the volumes of a sphere with a diameter of 6 centimeters (cm) and a cylinder with a diameter of 6 cm and height of 6 cm. Determine the volume of each figure to the nearest cubic centimeter. Which solid figure has the greater volume? Volume of sphere = 4 πr3 3 Show your work. Sphere ___________ cm3 Cylinder___________cm3 ___________________ has a greater volume