Geometry 1-2 est #7 Review Name Date Period State if each pair of triangles is similar. If so, state how you know they are similar (AA, SAS, SSS) and complete the similarity statement. 1) Q R 2) V F H F G HGF ~ similar; AA similarity; HQR E W EFG ~ not similar G 3) W 4) V V K L U K KLM ~ M similar; SAS similarity; KVW L UV ~ similar; SSS similarity; KL Find the missing length indicated. Solve for x. 5) 6)? x
Find the missing length indicated. 7) Solve for x. 8)? x Find the missing length indicated. Solve for x. 9) 10)? x Find the EXAC value of each trigonometric function indicated. 11) sin 12) tan 13) csc 14) cos 15) cot 16) sec
Name each figure in as specific a manner as possible. 17) 18) triangular prism trapezoidal prism 19) square prism 20) rectangular prism 21) 22) pentagonal prism Find the volume of each right rectangular prism. hexagonal prism 23) 24) 25) 4 ft 144 ft³ 12 yd 3 yd 12 yd 4 ft 26) 108 mi³ 11 km 3 mi 8 km 2 km 12 yd 12 yd 432 yd³ Find the surface area of each right rectangular prism. 2 km 176 km³ 11 km 27) 12 cm 12 cm 28) 8 m 12 m 592 m² 7 cm 10 m 12 cm 12 cm 624 cm² 12 m 10 m 29) 2 mi3 mi 92 mi² 30) 2 cm 120 cm² 8 mi 8 mi 3 mi
Find the area of each triangle. Round your answers to the nearest tenth. 31) D 32) 6 m 76 4 ft 46 E 10 m F 21.6 m² S 41 10.5 ft² R 33) X 34) S 62 4 yd 65 Z 6.2 yd² 53 Y 26.4 ft² 9 ft R Find and label the missing angles and sides for each triangle. Round your answers to the nearest tenth. 35) 36) B 16 A 29 61 14 7.7 C A 7.5 41 10 C 6.6 49 B Find the EXAC value of each trigonometric function indicated. 37) Find sec if sin 38) Find csc if cot Find the area of each regular polygon. Round your answers to the nearest tenth. 39) 40) Perimeter = 48 mi mi² Perimeter = 28 ft ft²
41) In the figure below, what is the probability that a randomly-selected point lies in the shaded region? Area of circle = π(4) 2 = 16π Area of each triangle = (½)(4)(4) = 8 Shaded area = 16π 8 8 = 16π - 16 Ratio of shaded to entire circle = (16π 16) / 16π = (π 1) / π 42) In the figure below, what is the probability that a randomly-selected point lies in the shaded region? Area of larger circle = π(7) 2 = 49π Area of smaller circle = π(4) 2 = 16π Shaded area = 49π - 16π = 33π Ratio of shaded to entire circle = 33π / 49π = 33 / 49 43) What is the definition of skew lines? Non-coplanar lines that do not intersect 44) What is the definition of a dihedral angle? he figure formed by two intersecting planes or two half-planes with a common edge 45) Name the five platonic solids. etrahedron (triangular pyramid), Hexahedron (cube), Octahedron, Dodecahedron, Icosahedron 46) What is the definition of a face of a geometric solid or other three-dimensional figure? An individual surface 47) What is the definition of an edge of a geometric solid or other three-dimensional figure? he intersection of two faces of a figure; it is a segment that joins two vertices 48) What is the definition of a vertex of a geometric solid or other three-dimensional figure? A point (or corner) where two or more segments meet 49) With regard to a three-dimensional figure, what is a net? A two-dimensional pattern that can be "folded" to form a three-dimensional figure; an "unfolded" polyhedron
50) a. How many faces does a cube have? 6 b. How many bases does a cube have? 2 c. How many sides does a cube have? 4 d. How many edges does a cube have? 12 e. How many vertices does a cube have? 8 51) a. How many faces does a triangular prism have? 5 b. How many bases does a triangular prism have? 2 c. How many sides does a triangular prism have? 3 d. How many edges does a triangular prism have? 9 e. How many vertices does a triangular prism have? 6 f. What is the shape of the sides of a right triangular prism? Rectangles 52) If a right rectangular prism has a length of ten centimeters, a width of seven centimeters, and a height of twelve centimeters, what is the length of a diagonal of the prism? 17.12 centimeters (approximately) 53) A flat work of art in the shape of a triangle is hanging on a wall. he length of side one of the artwork is 14 inches, the length of side two is 19 inches, and side three is 16 inches long. a. What is the perimeter of the work of art? 49 inches b. What is the area of the work of art? 12026.4375 square inches c. What are the measures of all three angles formed by the work of art? 55.54 degrees (approximately) 46.18 degrees (approximately) 78.28 degrees (approximately) 54) A real estate agent has just taken a trigonometry class at a local community college. He is considering purchasing a piece of land and is waiting to see the surveyor s report before closing the deal. If the surveyor submits the drawing shown below, explain why the agent might want to reject the sale. Based on the diagram labels, this is an ambiguous case of the Law of Sines, so it's possible that the 370-foot side of the land may actually swing inward, resulting in a smaller property. 400 feet 370 feet 71º