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Grade 8 Unit 3 Common Assessment Name____________________________ Date_____________ 8. G.2/8.G.4 1. Rectangle P is dilated about the origin with a scale factor of 0.5 and then reflected over the y-axis. The new image is Rectangle T. Which statements are true about Rectangle P and Rectangle T? A. They are congruent but not similar because dilation with a scale factor other than 1 changes the lengths of the sides but not the shape of the figure. ☐ TRUE ☐ FALSE B. They are similar but not congruent because dilation with a scale factor other than 1 changes the lengths of the sides but not the shape of the figure. ☐ TRUE ☐ FALSE C. They are congruent and similar because the rigid motion did not change the size or shape of the figure. ☐ TRUE ☐ FALSE D. They are neither congruent nor similar because the rigid motion changed the size and the shape of the figure. ☐ TRUE ☐ FALSE 8.G.5/8.EE.7 2. A. Find the measure of angle A. ☐ 9° ☐ 63° ☐ 77° ☐ 117° Joliet Public Schools District 86 | Common Assessment 2014-15, Grade 8, Unit 3 1 B. Justify the steps you took to solve Part A. 8. G. 5 3. Read the problem and evaluate Melinda’s method for finding the missing angle. Explain why Melinda’s answer is incorrect and correct her error. ? 150° 85° I solved the problem by first subtracting 150° from 180° to find the measure of the angle adjacent to the 150° angle, because I know that the sum of the measures of two angles that make a straight line equal 180°. Next, I added two remote interior angles because I know the sum of the measures of two remote interior angles are equal to the measure of the exterior angle. The missing angle is 235° Joliet Public Schools District 86 | Common Assessment 2014-15, Grade 8, Unit 3 2 8. G.1 4. Parallelogram ABCD is shown on the coordinate plane. A. Rotate Parallelogram ABCD 180 clockwise about the origin and plot Parallelogram EFGH on the coordinate plane. B. Identify the coordinates for each image on the coordinate plane. Coordinates E F G H C. Select all the following statements about Parallelogram ABCD and Parallelogram EFGH on the coordinate plane above that are true. ☐ ☐ ☐ ☐ ̅̅̅̅̅ ̅̅̅̅ ☐ ̅̅̅̅ ̅̅̅̅ ☐ ̅̅̅̅ ̅̅̅̅ ☐ ̅̅̅̅ ̅̅̅̅ ☐ Joliet Public Schools District 86 | Common Assessment 2014-15, Grade 8, Unit 3 3 8. G.3 5. Kelly and Jake are working together on the sequence of transformations that occurred on the coordinate plane below. Kelly says that the pre-image was reflected over the y axis followed by a reflection over the x-axis. Jake says the pre-image had to be reflected over the x-axis followed by the a reflection over the y-axis. Kelly and Jake turn to Mark to settle the argument. Mark says they are both right and the teacher agrees with Mark. A. Explain how they can both be right about the sequence of transformations. You may use words, drawings or tables to justify your explanation. B. Ian says there is another way to describe the transformation that Kelly, Jake and Mark are examining on the coordinate grid above. Describe another sequence or type of transformation that would have the same results as above. Joliet Public Schools District 86 | Common Assessment 2014-15, Grade 8, Unit 3 4 8. G.3 6. A. Identify the sequence of transformations that could take ∆ XYZ to ∆ X’Y’Z’ ☐a reflection across the x-axis followed by a translation of 2 units to the right ☐ a rotation 180° clockwise about the origin followed by a translation of 7 units up ☐ a translation of 2 units to the right followed by a rotation 90° clockwise about the origin ☐ a reflection across the y-axis followed by a translation of 3 units down 8.G 2 B. Select all statements that are true about the transformation above. ☐ All congruent figures are similar because they have a scale factor of 1. ☐ All similar figures are congruent because they have a scale factor of 1. ☐ The triangles are not similar because the pre-image was dilated by a scale factor of 1. ☐ The triangles are congruent because the pre-image was dilated by a scale factor of 1. 8. G.3 Joliet Public Schools District 86 | Common Assessment 2014-15, Grade 8, Unit 3 5 7. Apply a dilation by a scale factor of centered at the origin and record the new image’s coordinates in the table. Coordinates S’ R’ Q’ 8. G. 4 8. Determine if the triangles are similar. Justify your answer. 8. G.5/8. EE.7 Joliet Public Schools District 86 | Common Assessment 2014-15, Grade 8, Unit 3 6 9. A. Given each angle. and solve for x and find the measure of X = _______ 8.G.5 10. Determine if each of these statements is always true, sometimes true, or never true. A. A triangle can have 2 right angles. ☐ sometimes true ☐ always true ☐ never true B. Alternate exterior angles of parallel lines cut by a transversal are congruent . ☐sometimes true ☐always true ☐ never true C. Same side exterior angles of parallel lines cut by a transversal are supplementary. ☐sometimes true ☐always true ☐never true D. If the measure of an angle is represented by x, then the measure of its supplement is represented by 180-x. ☐sometimes true ☐always true ☐never true E. If a pair of triangles has two congruent angles, the triangles are similar. ☐sometimes true ☐always true ☐never true 8. G.2 Joliet Public Schools District 86 | Common Assessment 2014-15, Grade 8, Unit 3 7 11. A sequence of transformations was applied to an equilateral triangle in a coordinate plane. The transformations used were rotation, reflections, and translations. Which statement about the resulting figure is true? ☐ It must be an equilateral triangle with the same side lengths as the original triangle. ☐ It must be an equilateral triangle but the side lengths may differ from the original triangle. ☐ It may be a scalene triangle, and all the side lengths may differ from the original triangle. ☐ It may be an obtuse triangle with at least one side the same length as the original triangle. 8. G.5 12. In the figure, p ll q. Which of these statements is not true? ☐ 2 and 6 are congruent because corresponding angles are congruent. ☐ 2 and 7 are supplementary because same side exterior angles are supplementary ☐ 6 and 5 are congruent because same side interior angles are congruent ☐ 1 and 7 are congruent because alternate exterior angles are congruent ☐ 3 and 5 are congruent because alternate interior angles are congruent ☐ 4 and 5 are supplementary because same side interior angles are supplementary Joliet Public Schools District 86 | Common Assessment 2014-15, Grade 8, Unit 3 8