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Assessment Bank: Linear Algebra Focus 1-3 Note: This is not a unit test. These are items aligned to the 3 on the learning scale for the unit(s). 1) Given the two congruent triangles below, describe a sequence of transformations that would “move” one triangle exactly onto the other. Be sure to include any reflections, centers and angles of rotation, and directions and distances of translations. (8.G.A.1) 2) Provide the minimum amount of information needed to guarantee that these two triangles are congruent. (Note: The information needed is a list of measurements.) (8.G.A.2) 3) Under a particular transformation, point A’ is the image of point A and point B’ is the image of point B. a) Give a detailed description of the transformation. (8.G.A.1) b) Use a ruler and an angle ruler or protractor to help you draw the image of trapezoid ABCD under the transformation you described in part (a). (8.G.A.1) c) Are the pre-image and the image congruent? Explain why or why not. (8.G.A.2) 4) The large triangle below is made from congruent triangles. a) If you moved Triangle 1 onto Triangle 2, which vertices would match? (8.G.A.1) b) Carefully describe a combination of transformations that would move Triangle 1 onto Triangle 2. You may add lines or points to the diagram. (8.G.A.2) 5) Use the graph below. a) Describe a sequence of reflections that transforms ABCD to image A’B’C’D’ (8.G.A.2) b) Describe a rotation that transforms ABCD to image A’B’C’D’ (8.G.A.2) c) Describe how the rotation in part (b) affects the coordinates of vertices A, B, C, D (8.G.A.3) 6) The diagram below shows PQRS on a coordinate plane. Justify how PQRS was transformed to P’Q’R’S’ (8.G.A.3) 7) The diagram below shows PQRS on a coordinate plane. Justify how PQRS was transformed to P’Q’R’S’ (8.G.A.3) 8) The diagram below shows PQRS on a coordinate plane. Justify how PQRS was transformed to P’Q’R’S’ (8.G.A.3) 9) The diagram below shows PQRS on a coordinate plane. Justify how PQRS was transformed to P’Q’R’S’ (8.G.A.3) 10)Three triangles are graphed on the coordinate grid. Show evidence that Triangle 1 and Triangle 2 are congruent by finding one or more transformations that would move Triangle 1 to the exact position of Triangle 2. Give complete descriptions of these transformations. (8.G.A.3) 11. Find the measure of each angle in the diagram below. BAC ______ ACB ______ Directions: In diagram below line x is parallel to line y. Use the diagram to answer questions 2 through 6. 12. Name a pair of alternate interior angles. 13. Name a pair of corresponding angles. 14. Name a pair of alternate exterior angles. 15. Find the measure of each angle in the diagram. a ______ f______ b ______ g ______ n ______ p ______ c ______ d ______ e ______ h ______ k ______ m ______ r ______ t ______ v ______ 16. Explain how you found the measure of m. Jack drew the triangle to the right in the Match Game. 17. Which measurements of angles and sides can he give partner to ensure that she draws a congruent triangle? his 18. What two measurements can he give his partner to ensure that she draws a similar triangle? Directions: In diagram below PQ is parallel to RS. Use the diagram to answer questions 19 and 20. 19. Name another angle whose measure is 76˚. 20. Explain how you know this angle has the same measure. 21. Look at the figure on the coordinate grid. On the same coordinate grid, draw a figure similar but NOT congruent to the provided. that is figure 22. Show that triangles 1 and 2 are congruent by finding one or more transformations that would move triangle 1 to the exact position of triangle 2. Give a complete description of these transformations. Directions: Use the following diagram and information for questions 23 through 24. 23. Is triangle 1 similar to triangle 3? ______ If so, how can you tell? _________________ ___________________________________ ___________________________________ 24. What is the scale factor? _____________ Directions: Use the following diagram and information for questions 25 through 28. An engineer decides to use similar triangles to find the distance across the river. He makes the diagram shown. 25. Which triangles appear to be similar? B current bridge new bridge A 26. What must the engineer know about these triangles to conclude they are similar? 200 ft. C 250 ft. 150 ft. E 400 ft. D 27. Find the distance across the river from point B to point A. Explain how you found your answer. 28. Why does BC have the same slope as CD?