Foundations of Math 2: Review for Benchmark #3 Foundations of Math 2

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1 Foundations of Math 2: Review for enchmark #3 Foundations of Math 2 Name: ate: 1. Which of the following is not a proper way to name the angle shown below? 4. The diagram below shows angles formed by intersecting lines ngle XYZ is shown. Which answer reflects the relationship between 2 and 3?. 2 and 3 are vertical angles.. 2 and 3 are corresponding angles.. 2 and 3 are alternate exterior angles.. 2 and 3 are adjacent supplementary angles. Which point lies in the interior of angle XYZ?. point V. point W. point X. point Y 3. Look at the drawing below. 5. What is the supplement of a 40 angle? Use the diagram below to answer the question. Note: The figure is not drawn to scale. What is the measure of angle? What is the measure of x? page 1

2 7. ngle J and angle K are vertical angles, as shown in the figure below. 10. hoose the correct solution for the equation: 5x + 8 = 43. x = 10. x = 7. x = 175. x = What is the solution to the equation below? 3(x 4) = 5x 6. x = 3. x = 3 4. x = 1. x = 9 The measure of angle J is 46. What is the measure of angle K? In the figure below, intersects at point. 12. What value of x makes the equation below true? x = If the coordinates of are (3, 4) and the coordinates of are ( 3, 4), then the length of is What is the measure of? In the accompanying diagram, line a intersects line b. What is the value of x? What is the value of x in the triangle shown above? What is the midpoint of the line segment connecting the points ( 2, 4) and (5, 2)?. ( 32, 1 ). ( 3, 3 2 ). ( 72, 1 ). ( 32, 2 ) Foundations of Math 2 page 2 Foundations of Math 2: Review for enchmark #3

3 16. In the graph below, figure M was rotated clockwise about the origin to generate figure T. 18. Study RST on the grid below. What was the angle of rotation of figure M about the origin? Renee drew triangle on a coordinate grid. Then she used one transformation of triangle to create triangle, as shown below. When RST is translated 4 units down, what are the apparent coordinate of T?. ( 8, 1). ( 4, 1). ( 1, 8). (0, 4) 19. If triangle is rotated 180 degrees about the origin, what are the coordinates of? Which transformation did Renee use to create triangle?. ilation. Rotation. Reflection. Translation. ( 5, 4). ( 5, 4). ( 4, 5). ( 4, 5) Foundations of Math 2 page 3 Foundations of Math 2: Review for enchmark #3

4 20. Use the figure below to answer the question that follows. 22. Look at PQR on this grid. graphic artist needs to reflect triangle across the x-axis to create Figure. What are the coordinates of?. (1, 2). (2, 1). ( 1, 2). ( 2, 1) 21. If quadrilateral QRST is reflected across the y-axis, what will be the coordinates of point Q? What are the coordinates of the image of point R after a 90 counterclockwise rotation about the origin?. ( 6, 2). ( 2, 6). (6, 2). (6, 2) 23. In the coordinate plane, right triangle XYZ is reflected over the line y = x.. ( 2, 4). ( 2, 1). ( 1, 2). ( 1, 4) What are the coordinates of the vertex of the right angle in X Y Z?. (3, 1). (3, 0). (1, 3). (1, 2) Foundations of Math 2 page 4 Foundations of Math 2: Review for enchmark #3

5 24. The vertices of are (2, 1), (3, 4), and (1, 3). If is translated 1 unit down and 3 units to the left to create EF, what are the coordinates of the vertices of EF? 28. In the figure below, is a right triangle and m = 40.. (0, 1), E(1, 2), F(1, 3). (0, 1), E(0, 3), F( 2, 2). ( 2, 2), E(0, 3), F( 1, 0). ( 1, 0), E(0, 3), F( 2, 2) 25. What are the coordinates of the image of point P(1, 4) after a clockwise rotation of 90 about the origin?. (4, 1). (4, 1). (1, 4). ( 1, 4) What is m E? What is m x? 26. What value of x would make the equation 2 3 = 8 x true? right triangle is shown below What is the value, in degrees, of x? Foundations of Math 2 page 5 Foundations of Math 2: Review for enchmark #3

6 30. The diagram below shows three intersecting lines. 32. Use the triangle to answer the question. Triangle PQR is a scalene right triangle. Which of the following is correct?. cos P = r p. sin Q = q p. cos P = p r. tan Q = q p ased on the measurements in the diagram, what is x? 33. In the accompanying diagram, m = 32 and = 10. Which equation could be used to find x in? Triangle is shown below.. x = 10 sin 32. x = 10 cos 32 What is the cosine of angle?. x = 10 tan 32. x = 10 cos Foundations of Math 2 page 6 Foundations of Math 2: Review for enchmark #3

7 34. ladder leaning against a house is shown below. 36. Right triangle JKL is shown below. Note: The figure is not drawn to scale. Note: The figure is not drawn to scale. What is the distance (x) from the base of the ladder to the house? Round the answer to the nearest foot.. 13 feet. 17 feet. 21 feet. 36 feet What is the measure of J? Round the answer to the nearest degree In the accompanying diagram of right triangle, a right angle is at, = 26, and m = 27. Find the length of to the nearest tenth. 35. lighthouse, which is 18 feet high, stands on a cliff that is 150 feet above sea level. The distance from the top of the lighthouse to a sailboat on the ocean is 360 feet. 38. In right triangle shown below, = 18.3 and = Note: The figure is not drawn to scale. What is the angle of elevation (x) from the sailboat to the top of the lighthouse? Round the answer to the nearest degree What is the measure of, to the nearest tenth of a degree? Foundations of Math 2 page 7 Foundations of Math 2: Review for enchmark #3

8 39. In the diagram below, E = E. 42. In the accompanying diagram, is similar to EF with = and = E. If = 4.5, = 4, F = x, and E = 5, find the value of x. Which statement is not always true?. =. E = E. E = E. E = E 40. Triangle is shown in the diagram below. 43. If triangles EFG and JKL are congruent, then which two segments must be congruent? If E joins the midpoints of and E, which statement is not true?. E = 1 2. E. = E. E 41. In the accompanying diagram, QRS is similar to LMN, RQ = 30, QS = 21, SR = 27, and LN = 7. What is the length of ML?.. EF and JK. EF and JL FG and JK. FG and JL Foundations of Math 2 page 8 Foundations of Math 2: Review for enchmark #3

9 44. Triangles GHJ and KLM are congruent. The triangles and some of their angle measures are shown in the diagram below. 46. Which theorem can be used to prove that the triangles in the figure below are congruent?. side-by-side (SSS). side-angle-side (SS). angle-side-angle (S). angle-angle-side (S) ased on the angle measures in the diagram, what is m JGH? 47. Which theorem of congruence should be used to prove QRS = TUV? In the diagram below, triangle FHG is congruent to triangle XZY.. ngle-side-ngle (S). ngle-ngle-side (S). Side-ngle-Side (SS). Side-Side-Side (SSS) What is the measure of angle X? Foundations of Math 2 page 9 Foundations of Math 2: Review for enchmark #3

10 48. In the diagram below, RT intersects QU at point S. 50. an we prove LMN is congruent to XYZ? Is so, which postulate can we use to do so? Which postulate should be used to prove that RQS = TUS?. Side Side Side. ngle Side ngle. ngle Side Side. Side ngle Side 49. Given: and intersect at point E; 1 = 2. Yes, we can prove they are congruent using the SS postulate.. Yes, we can prove they are congruent using the S postulate.. No, we cannot prove they are congruent because XYZ appears to be a right triangle and LMN is not a right triangle.. No, we cannot prove they are congruent because none of the three postulates can be used. Which theorem or postulate can be used to prove E E?.. SSS. S. SS Foundations of Math 2 page 10 Foundations of Math 2: Review for enchmark #3

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