Name ________________________________ Class___________ Score________

© Exceeding the CORE Standards Based Assessments 1

GEOMETRY (8.G.1) Verify experimentally the properties of rotations, reflections, and translations…

1. In triangle PQR, m∠P = 30°, m∠Q = 90°, and m∠R = 60°. If the triangle is rotated 90° clockwise about a point, what is the measure of the image of ∠P?

2. Triangle ABC represents the location of a flower bed in Ms. Grant’s garden. Ms. Grant translates this triangle 5 units left and 2 units down to show the location of a second flower bed. The image is triangle A′B′C′. How long is side B′C′?

3. What quadrant would triangle M be in after a rotation of 90° counterclockwise about the origin?

4. Which of the following is not true of a triangle that has been reflected across the x-axis?

a) The new triangle is the same size as the original triangle.

b) The new triangle is the same shape as the original triangle.

c) The new triangle is in the same orientation as the original triangle.

d) D The x-coordinates of the new triangle are the same as the x-coordinates of the original triangle.

5. Sketch the image of the triangle under a reflection across the y-axis.

M

Name ________________________________ Class___________ Score________

© Exceeding the CORE Standards Based Assessments 2

GEOMETRY (8.G.2) Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. 1. A sequence of transformations was applied to

an equilateral triangle in a coordinate plane. The transformations used were rotations, reflections, and translations. Which statement about the resulting figure is true?

a) It must be an equilateral triangle, but the side lengths may differ from the original triangle.

b) It may be an obtuse triangle with at least one side the same length as the original triangle.

c) It may be a scalene triangle, and all the side lengths may differ from the original triangle.

d) It must be an equilateral triangle with the same side lengths as the original triangle.

2. Identify a sequence of transformations that will transform figure C into figure D.

3. Identify a sequence of transformations that will transform figure P into figure Q.

4. Identify a sequence of translations, reflections, rotations, and/or dilations transforms figure F into figure G?

5. Are quadrilaterals DEFG and LMNP congruent? If so, give a sequence of transformations that maps DEFG to LMNP. If not, explain.

Name ________________________________ Class___________ Score________

© Exceeding the CORE Standards Based Assessments 3

GEOMETRY (8.G.3) Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

1. Carla plots coordinates to represent the corners of her garden: D(3.5, 2.5), E(–3, 4), and F(–1, –4). She decides to quadruple the length of each side using the origin as the center for the enlargement of her garden. What is the location of F’?

2. How many degrees would you need to rotate a figure for the image to coincide with the preimage?

3. Which axis is point G(–x, y) reflected over to get G'(–x, –y)?

4. The logo for a school basketball team contains a triangle with vertices P(3, 9), Q(0, 6), and R(–3, –3). After a dilation, the image of P is P'(4, 12). What is the scale factor of the dilation?

5. A figure WXYZ has vertices W(0, 0), X(8, 0), Y(6, 4), and Z(2, 4). The figure is dilated by a scale factor of 0.5 and then translated 6 units right and 8 units up. Find the coordinates of figure W″X″Y″Z″.

Name ________________________________ Class___________ Score________

© Exceeding the CORE Standards Based Assessments 4

GEOMETRY (8.G.4) Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. 1. Triangle QRS was rotated 90° clockwise. Then

it underwent a dilation centered at the origin with a scale factor of 4. Triangle Q’R’S’ is the resulting image. Compare the perimeters of triangle QRS and triangle Q’R’S’. Explain your reasoning.

2. Rectangle C undergoes a dilation with scale factor 0.5 and then a reflection over the y- axis. The resulting image is Rectangle D. Which statement about Rectangles C and D is true? a) They are similar but not congruent. b) They are congruent and similar. c) They are congruent but not similar. d) They are neither congruent nor similar.

3. Quadrilateral LMNO is graphed on a coordinate plane. Amber reflected LMNO over the x-axis and then rotated it 90° clockwise about the origin. She labeled the final image WXYZ. Mason dilated LMNO by a scale factor of 3 and then translated the resulting figure 2 units left. He labeled the final image PQRS. Identify a pair of quadrilaterals from the three quadrilaterals LMNO, WXYZ, and PQRS that are similar but not congruent.

4. Trina makes 3 rectangular quilts for her grandchildren. The first measures 70 inches by 90 inches. She enlarges these dimensions by a scale factor of 1.2 to make a second quilt. Then she enlarges the dimensions of the second quilt by a scale factor of 1.5 to make the third quilt. What are the dimensions of the third quilt?

5. The triangle formed by a 4-foot-tall mail box and its 6-foot shadow is similar to the triangle formed by a utility pole and its 15-foot shadow at the same time of day. What scale factor is used to transform the image of the utility pole triangle from the preimage of the mailbox triangle? Use this scale factor to determine the height of the utility pole.

Name ________________________________ Class___________ Score________

© Exceeding the CORE Standards Based Assessments 5

GEOMETRY (8.G.5) Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

1. Triangle P is similar to triangle Q. Triangle P has two angles with measures of 41° and 82°. Which two angle measures could be included in triangle Q?

a) 41° and 58° b) 41° and 74° c) 82° and 57° d) 82° and 98°

2. Gold Street and York Street are parallel. Ocean Avenue crosses each of them. The city planner needs to find the measures of the angles at each intersection. Find the measures of the labeled angles.

3. Lines 𝑎 and 𝑏 are parallel and cut by the transversal 𝑐. Find the value of 𝑥.

4. A triangular flower bed has the angle measures shown. What is the value of x?

5. Quadrilateral ABCD is a parallelogram. Given m∠ADC = (𝑥 – 20)°, what is the value of 𝑥? Given m∠EBC = 4𝑦 °, what is the value of 𝑦?

Name ________________________________ Class___________ Score________

© Exceeding the CORE Standards Based Assessments 6

GEOMETRY (8.G.6) Explain a proof of the Pythagorean Theorem and its converse.

1. Find the length of the missing side of the triangle. Round your answers to the nearest tenth.

2. Janet is buying edging for a triangular flower garden she plans to build in her backyard. If the lengths of the three pieces of edging that she purchases are 12 feet, 9 feet, and 6 feet, will the flower garden be in the shape of a right triangle? Explain.

3. A rectangular picture frame has dimensions 9 inches by 12 inches. The diagonal of the frame is 15 inches. Do the sides of the frame meet at a right angle? Explain.

4. Find the length of the missing side of each triangle.

5. Miley, Jugo, and Casper are throwing a Frisbee. Miley is 19.5 feet away from Jugo. Jugo is 32.5 feet away from Casper. Casper is 26 feet away from Miley. Do the distances between Miley, Jugo, and Casper form a right triangle? Explain.

48 in.

20 in.

Name ________________________________ Class___________ Score________

© Exceeding the CORE Standards Based Assessments 7

GEOMETRY (8.G.7) Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

1. Ms. Whitney can take two routes from her home to the post office. The solid segments show the route she would take when she drives along city roads. The dotted segments

show a shortcut she could take when she bikes through the woods. How much farther will Ms. Whitney travel by car than by bike?

2. What is the approximate length of the diagonal from point A to point B in the right rectangular prism shown? Round your answer to the nearest centimeter.

3. A school gym is rectangular with a length of 60 feet and a width of 30 feet. For warm-up, Beverly runs along the diagonal of the gym from one corner to the other. Mark runs the length and width of the gym to the opposite corner. How much farther did Mark run? Round to the nearest tenth.

4. The diagram shows how a wood beam broke. How long was the beam originally?

5. A 38-foot ladder is leaning against a building. The bottom of the ladder is 7 feet from the base of the building. To the nearest foot, how high does the ladder reach on the building?

Name ________________________________ Class___________ Score________

© Exceeding the CORE Standards Based Assessments 8

GEOMETRY (8.G.8) Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

1. The vertices of a triangle have coordinates 𝐷(2, 3), 𝐸(– 1, 0), and 𝐹(– 6, 7). Is this a right triangle? Justify your answer.

2. Cheryl is mountain biking and maps his route on a coordinate plane. She starts at the origin and then rides 5 miles east, 2 miles north, 1 miles east again, and 4 miles south. What are the coordinates of Chery’s endpoint?

3. What is the length of line segment ST with endpoints S(2, 4) and T(7, 16)?

4. Find the length of the hypotenuse to the nearest tenth.

5. When a coordinate grid is superimposed on a map of Lanesville, the middle school is located at (15, 23) and the library is located at (27, 9). If each unit represents 1 mile, how many miles apart are the middle school and the library? Round your answer to the nearest tenth.

Name ________________________________ Class___________ Score________

© Exceeding the CORE Standards Based Assessments 9

GEOMETRY (8.G.9) Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

1. A water tank is in the shape of a right circular cylinder with a height of 15 feet and a volume of 375𝜋 cubic feet. What is the diameter, in feet, of the water tank?

2. A cone has a radius of 2.3 inches and a height of 3.1 inches. What is the volume, to the nearest tenth of a cubic inch, of the cone?

3. A cylinder has a diameter of 14 centimeters and a volume of 323 cubic centimeters. What is the height, to the nearest tenth of a centimeter, of the cylinder?

4. An above-ground swimming pool in the shape of a cylinder has a diameter of 16 feet and a height of 5 feet. If the pool is filled with water to 1.5 feet from the top of the pool, what is the volume, to the nearest cubic foot, of the water in the pool?

5. Ice cream completely fills the cone and the hemisphere above the cone. What is the slant height of the cone?