3 rd quarter Review Name: Date: 1.] The longest side of a right triangle is called the.. leg. hipponamoose. hypotenuse D. ig Guy 2.] The acute angles of a right triangle are always.. congruent. complementary. supplementary D. cute little things 3.] Greek mathematician discovered and proved an important theorem about right triangles that allows us to find a missing side of a right triangle when the other two sides are known. His name was.. Ralph. Murgatroid. Mr. Whydidhedothatdontwehaveenoughtolearn D. Pythagoras 4.] Use the famous theorem from #3 to find the value of x in the following diagram. Round your answer to the nearest hundredth.. 10.25. 15.26. 21.00 D. 56.00 13 8 x 5.] Find the value of y. Round your answer to the nearest tenth. (Hint: Use the ig Guy s theorem again!). 13.6. 14.0. 14.2 D. 26.4 y 21 16 6.] The length of a rectangle is 2 inches and the width is 1 inch. Find the diagonal of the rectangle.. 3 inches. 5 inches. 25 inches D. 3
7.] The measure of each leg of an isosceles right triangle is 3. Find the hypotenuse of the triangle.. 2 3. 3 3 2 3 2 D. 2 3 3 8.] Find the length of a side of the square in the diagram.. 5. 2 5. 5 2 D. 10 2 10 9.] Find the values of a and b.. a 3 3, b 6 3. a 9, b 9 2. a 9 3, b 18 D. a 18, b 9 3 a 9 b 60 10.] is an equilateral triangle with side 10. Find the length of the altitude, x. 10. 5. 10. 5 2 D. 5 3 x 11.] Which of the following could be the sides of a right triangle?. 5, 6, 7. 5, 10, 12. 5, 12, 13 D. 9, 10, 14 12.] Which of the following could be the sides of an acute triangle?. 5, 6, 7. 5, 10, 12. 5, 12, 13 D. 9, 10, 14 13.] Which ratio should be used to find tan?. a b. a c. b c D. b c a
14.] Find tan. Round your answer to four decimal places.. 0.3846. 0.4167. 0.9231 D. 2.4000 10 26 24 15.] Find the value of x.. 9.18. 13.11. 0.04 D. 27.90 16 x 35 16.] Find the measure of Z. X. 48.6. 28.1. 61.9 D. 41.4 17 Y 15 Z Use the diagram below for questions 17-21. Watch labels! hoose the answer from the following:. radius. chord. diameter D. secant E. tangent 17.] D is best described as a. D E F 18.] E is best described as a. G 19.] line G is best described as a. 20.] line DF is best described as a. 21.] D is best described as a.
Use the following diagram for questions 22-26. 22.] Find the measure of arc.. 55. 45. 35 D. 125 55 23.] Find the measure of arc D. E D. 55. 90. 35 D. 125 24.] Find the measure of arc E.. 180. 125. 145 D. 215 25.] rc ED is a.. minor arc. semicircle. major arc D. hemisphere 26.] If E = 5x + 12 and D = 6x 4, then the radius of the circle is.. 8. 16. 46 D. 92 Use the following circle with center O for questions 27-29. 27.] Find the measure of O.. 70. 90. 140 D. 280 12 O 140 12 28.] Find the measure of.. 70. 90. 140 D. 280 29.] Find the measure of arc.. 220. 180. 140 D. 110
Use the following diagram, showing circle O with tangents R and R for questions 30-32. 30.] Find the measure of OR.. 45. 90. 100 D. 130 225 O 10 24 31.] Find the length of tangent R.. 5. 10. 12 D. 24 R 32.] Find the length of RO.. 14. 26. 34 D. 36 30. Lookout towers are located at points,, and on the section of a national forest shown in the drawing. Which of the following statements is true concerning formed by the towers? 4,123 m 5,385 m 4,472 m a. m is the greatest b. m is the least c. m is the greatest d. m is the least
30. From a point 22 feet from the base of a tower, a wire is stretched to an attachment 44 feet up the tower. To the nearest foot, how long is the wire? 44 feet 22feet 50. Three boats are anchored in a bay. Given the information in the diagram, which of the following statements concerning the distances between the boats is true?. <. <. < D. < 61 o 71 o
51. On the shores of a river, surveyors marked locations, and. The measure of = 40 degrees and the measure of = 105 degrees. Which lists the distances between these locations in order, least to greatest? Explain your reasoning. a. to, to, to b. to, to, to c. to, to, to d. to, to, to 52. Given: D D Which could be used to prove D D? D. SSS If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent.. SS If 2 sides and the angle between them in one triangle are congruent to 2 sides and the angle between them in another triangle, then the triangles are congruent.. S If 2 angles and the side of one triangle are congruent to 2 angles and the of another triangle then the 2 triangles are congruent. D. S If 2 angles and a side not between them are congruent to 2 angles and a side not between them of another triangle, then the triangles are congruent.
1.) The ratio of the measures of the angles of a 2.) Two similar rectangular rugs have a triangle is 7:14:15. Find the measure of each angle. scale factor of 2:3. The smaller rug has a perimeter of 24 feet. Part 1: Find the larger rugs perimeter: 3.) The ratio of the perimeter of ΔU to the perimeter of ΔV is 1:2. If the triangles are similar, what is the value of x + y? x + y = Part 2: What is the ratio of their areas? 4.) Triangles and DEF are similar and 5.) Given: ΔRSW ~ ΔTUW. Which have measurements as shown. proportion is ture? What is the measure of EF? EF = 6.) Given: ΔPQR ~ ΔWUN; m R is 78 7.) Given: Δ ~ ΔLMN. What is the measure of W? What is the length of? m<w = x = and =
8.)Which drawing contains a pair of similar triangles? State the postulate or theorem used? 9.) Which pair of triangles is similar? State the postulate or theorem used?.. 61. 6 D. Post/Thm: Post/Thm: 10.) Given DE is parallel to, 11.) If ΔD ~ ΔEF, find the value of h? D = 6, D = 12 and DE = 4, D what is? F E = h =
12.) In the diagram below of, 13.) triangle has sides whose lengths are which reason justifies the conclusion 6, 8, and 10. Give the side lengths a similar that? triangle could have. S SS D SSS Side lengths: 14.) girl 160 cm tall, stands 360 cm from a lamp post 15.) Triangles DE and NOP are similar. at night. Her shadow from the light is 90 cm long. The perimeter of the smaller triangle DE is How high is the lamp post? (draw a diagram and solve 133. The lengths of two corresponding sides on the triangles are 53 and 212. What is the perimeter of NOP? Height of the lamp post: Perimeter of NOP: 14.) Triangles EFG and QRS are similar. 15.) Triangles DE and NOP are similar. The length of the sides of EFG are 144, 128, and 112. The perimeter of the smaller triangle DE is The length of the smallest side of QRS is 280, 133. The lengths of two corresponding What is the length of the longest side of QRS? sides on the triangles are 53 and 212. (draw a diagram and solve) What is the perimeter of NOP? Length of the longest side: Perimeter of NOP: