Benchmark Test 4. Pythagorean Theorem. More Copy if needed. Answers. Geometry Benchmark Tests
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1 enchmark LESSON Tests More opy if needed enchmark Test 4 Pythagorean Theorem 1. What is the length of the hypotenuse of a right triangle with leg lengths of 12 and 6?. 3 Ï } 2. Ï } Ï } 3 D. 6 Ï } 5 2. Find the unknown side length of the right triangle. Write your answer in simplest radical form n equilateral triangle has a height of 8. What is the side length? Ï} 5 } 5. 8Ï} 3 } 3. 16Ï} 5 } 5 D. 16Ï} 3 } 3 4. n isosceles right triangle has leg lengths of 4 cm. Find the length of the hypotenuse. Round your answer to one decimal place. 5. The length of one leg of a right triangle is 10 cm and the length of the hypotenuse is 20 cm. Find the length of the other leg. Write your answer in simplest radical form. 6. Find the unknown side length of the right triangle using a Pythagorean triple. State the Pythagorean triple used. 50 cm 14 cm 7. Which of the following is not a Pythagorean triple or a multiple of a Pythagorean triple?. 10, 24, , 72, 75. 8, 10, 12 D. 5, 12, Decide if the segment lengths 7, 11, and 18 form a triangle. If so, would the triangle be acute, right, or obtuse? 9. Decide if the segment lengths 49, 88, and 121 form a triangle. If so, would the triangle be acute, right, or obtuse? 24
2 10. What type of triangle has side lengths 25, 60, and 65?. cute. Right. Obtuse D. Not a triangle 11. Which side lengths do not form a triangle?. 3, 6, 9. 4, 6, 9. 4, 5, 6 D. 3, 4, 5 Right Triangles 12. Identify the similar right triangles in the diagram, and then find the value of X Y W 8 Z 13. Find the length of the altitude to the hypotenuse. If necessary, round to the nearest tenth ft 20.5 ft Use the diagram for Eercises P S 13.1 ft 14. PR 5 15, QR 5 9, and PQ Find SQ. If necessary, round to the nearest tenth D PR 5 12, PQ 5 9. Find PS. If necessary, round to the nearest tenth D PR 5 16, PQ Find SR. If necessary, round to the nearest tenth. R Q D
3 enchmark LESSON Tests More opy if needed 17. Find the value of. If necessary, round to the nearest tenth Find the length of the hypotenuse. Write your answer in simplest radical form Find the lengths of the legs cm cm. 4 Ï } 2 cm. 2 Ï } 2 cm D. 8 Ï } 2 cm 20. Find the values of and y. Write your answer in simplest radical form. Sine, osine, and Tangent y Use the diagram for Eercises Find tan and tan. Round to four decimal places. 22. Find sin and sin. Round to four decimal places. 23. Find cos and cos. Round to four decimal places
4 24. Find the value of. Round to the nearest tenth Which epression can be used to find? a.. 15 tan tan 52. tan 52 } 15 D. tan 38 } 15 29b. 26. Find the values of and y. Round to the nearest tenth. y Which epression can be used to find?. 20 sin cos 65 } cos 65 D. sin 65 } You sled down a hill that is 15 meters high. The angle of depression is 24. bout how far did you sled?. 6.1 m m m D m 29. rope from a stake to a tent is 13 yd long and has an angle of elevation of yd 27 a. How far is the stake from the tent? Round to the nearest tenth. b. t what height is the rope fastened to the tent? Round to the nearest tenth. 27
5 enchmark LESSON Tests More opy if needed 30. Use a calculator to approimate the measure of /M to the nearest tenth of a degree. 31. Which epression can you use to find m/g? M 45 N 32 L G z y 34. F H 35.. tan 21 y }. cos 21 y } z. cos 21 } z D. sin 21 y } z 32. Solve the right triangle. Round decimal answers to the nearest tenth Solve the right triangle. Round decimal answers to the nearest tenth. Parallelograms The measures of three of the interior angles of a quadrilateral are 109, 114, and 75. What is the measure of the fourth interior angle? D Find the measures of an interior angle and an eterior angle of a regular heagon. 6 28
6 Use the diagram for Eercises z 1 13 (3 1 4) 7y 2 8 w y z Find the value of w in the parallelogram. 37. Find the value of in the parallelogram Find the value of y in the parallelogram. 39. Find the value of z in the parallelogram. 40. The diagonals of parallelogram D intersect at point E. What are the coordinates of E? D y 1 2 E , 5 } , 3 } , 3 } 2 2 D. 11, 5 } What theorem(s) can you use to show that the quadrilateral is a parallelogram? Eplain. D
7 enchmark LESSON Tests More opy if needed 42. For what value of is the quadrilateral a parallelogram? D Which of the following may not be true for a parallelogram to be a rhombus?. The diagonals are perpendicular.. The diagonals are congruent.. ll sides are congruent. D. Each diagonal bisects each pair of opposite angles. Special Quadrilaterals 44. Points Q(1, 2), R(2, 4), S(7, 21), and T(3, 0) form a quadrilateral. Determine whether QRST is a trapezoid. Eplain. 45. Trapezoid MNOP is isosceles. Find m/o N O M D In the diagram, } PQ is the midsegment of trapezoid EFGH. Find PQ. P E H 25 in. 33 in. 47. Points Q(0, 0), R(2, 4), S(4, 4), and T(4, 2) form a quadrilateral. Determine whether QRST is a kite. Eplain. G Q P F 30
8 48. Find m/ in the kite shown D D What is the most specific name for quadrilateral D? D. Rhombus. Kite. Square D. Parallelogram 50. quadrilateral has at least one pair of opposite angles congruent. What types of quadrilaterals meet this condition? 31
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