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Name: _____________________________ Geometry Final Exam Review Special Segments in Triangles (Ch. 5) Use the given diagram to solve for the variable and missing measures. 1) If MS is an altitude of MNQ, and m1 = 3x + 11, and m2 = 7x + 9, find the following: x = _____ m2 = ______ 2) If MS is a median of MSQ, and QS = 3x – 14, SN = 2x + 1, and mMSQ = 7x + 1, find the following: x = _____ SN = _____ QN = _____ 3) If WP is an angle bisector of WAH and mHWP = x + 12, mPAW = 3x – 2, and mHWA = 4x – 16, find the following: x = ______ mHWP = ______ mPAW = ______ 4) If WP is a perpendicular bisector of WAH, and mWHA = 8x + 17, mHWP = 10 + x, AP = 6y + 4, and PH = 22 + 3y, find the following: x = ______ mHWP = ______ y = ______ AH = ______ page 1 Quadrilaterals & Polygons (Ch. 6 and 11.1) I. Use the properties of parallelograms to complete the following. 1) Given: Parallelogram ABCD A 2) Given: BLUE is a rectangle. B L U y° (4x + 6)° x° (6x – 8)° (5y +16)° 56° D C B 3) E x = ________ x = ________ y = ________ y = ________ For questions a - c refer to Quadrilateral MIND. D a) If MIND is square, then m2 m3 = ___________ b) If MIND is a rectangle and DS = 7.5, then SM = __________ 7 If MIND is a rhombus and m NIM = 105°, then m1 = _________ N 5 S 1 c) 6 8 4 2 3 M II. 4) How do you find the interior angle sum of a polygon? 5) What is the sum of the exterior angles of a convex decagon? 6) What is the sum of the interior angles of a convex octagon? 7) What is the measure of one exterior angle of a regular nonagon? 8) A regular polygon has an interior angle that measures 165. How many sides does it have? 9) The sum of the measures of the interior angles of a certain convex polygon is between 6900 and 7100. How many sides does it have? 10) Is it possible for the interior angle of a regular polygon to equal 173? Why or why not? page 2 I Similarity & Proportion (Ch. 8) Determine whether the triangles are similar. If, Similar, state the similar triangles and tell which theorem or postulate was used. If not similar, write “none” in BOTH blanks. 35 L O G 1) 2) 20 15 97 14 A G 21 D A 9 6 16 97 9 R M N 15 R C CAR ~ ANM ~ ; by V 3) 4) ; by A G J 27 85 L O 27 8 68 Q 18 E T JLO ~ 12 M GAE ~ ; by ; by Find the value of x or y. Show your proportion. 5) 6) 20 x 12 3 6 14 y 9 Solve the proportions problems. Round answers to the nearest hundredth. 7) In a triangle the ratio of the measures of the 3 angles is 2:6:7. Find the measure of each angle. 8) A cable that is 72 ft. long needs to be divided into a ratio of 1:3. How long must each piece be? 9) A man 2.4 m tall, casts a 0.96 m shadow. At the same time, a flag pole casts a 4.8 m shadow. How tall is the flag pole? page 3 Special Right Triangles (Ch. 9) Solve by making a drawing for each problem. Leave all answers in simplified radical form. 1) If the bottom of a 13 ft. ladder is 5 ft. from the base of a wall, how far up the wall does the ladder reach? 2) The length of each side of an equilateral triangle is 10. Find the length of the altitude. 3) Find the length of the side of a square with a diagonal of length of 14. Solve for missing sides. Leave answers in simplified radical form. 4) 5) 45 x 6) x 7 8 30o x 2 3 7) 8) x x 30 6 3 4 9) 45 y 30 8 3 x 3 30 page 4 Trigonometry (Ch. 9) I. Use the diagrams to find each trigonometry ratio in simplest form. 1) cos B = __________ A 2) tan B = __________ 6 3) cos A = __________ 4) sin A = __________ 12 5) tan A =__________ C B 6 3 6) sin B = __________ II. Complete the following. Round all answers to the thousandths place or to the nearest degree. 7) sin 38 = __________ 9) cos __________ = 0.8572 11) tan 56 = __________ 8) cos 89 = __________ 10) tan __________ = 0.7824 12) sin 48 = __________ III. Trigonometric Ratios. Round all sides to the tenths place and angles to the nearest degree. 13) 14) 26 15) x x 3 7 x 18 38 57 24 Equation ______________ Equation ______________ Equation _____________ x = ____________ x = ____________ x = ____________ 16) 17 26 x 17) 18) x 14 23 9 37 x Equation ______________ Equation ______________ Equation _____________ x = ____________ x = ____________ x = ____________ page 5 IV. Draw a diagram, write an equation and solve. Round all answers to the hundredths place. 19) Ms. Euclid was so frustrated with her geometry test grades; she literally threw the test papers out her window. She knows that her window is 13 meters high from the ground. The angle of depression to see the papers is 27. How far away are the test papers from her apartment building? 20) Mrs. Long sees a cat stuck in a tree and decides to help it down. She is standing 21 feet away from the tree and the angle of elevation to the cat is 33. How high off the ground is the cat? Circles (Ch. 10) Find the indicated value in each of the following. Leave answers in simplified radical form. P B 6 F 3) C E D 2) 1) M A B E N Q R A S G C T 12 U PU RT mUT = 60 QT = 12 RT = _______ MN = 18 AE AB AE = 6 DC = ______ 4) 5) F Perimeter CFE = 46 AC = ______ 6) 7) x 45 100 B 120 150 x 30 D (2x 10) 41 150° A m AB = ______ x = ________ x = _______ x = _______ page 6 A 8) O 9) 70 (2y 10) E 155 mEAB = _______ B 7 B 52 (5x + 5) y = ______ C 10) m BD = _______ mBCD = _______ A x = ______ mCDB = _______ m CBD = _______ C D CB = _______ Suppose a chord of a circle is 24 inches long and is 9 inches from the center of the circle. Find the length of a radius. 11) x cm 4 cm 8 cm 5 cm x = _____________ page 7 Area and Perimeter (Ch. 11) A 1) 2) 20 cm 8 cm 3) 24 cm 45° DC = 14 m mABE = 30o 25 cm D E B 13 cm Area = _________ Area = _________ Area = _________ C 4 4) 5) 6 9 16 8 17 Area = _________ Area = _________ 6) If the area of a trapezoid is 252 cm2. If the lengths of the bases are 45 cm and 11 cm, find its height. 7) The area of a rhombus is 126 m2. If one diagonal measures 12 m, what is length of the other diagonal? page 8 Regular Polygons & Circles (Ch. 11) I. II. Make a drawing for each regular polygon and find the missing pieces: s side, a apothem, r radius, P perimeter, and/or A area. Leave #1 as exact answers (radical form) and round #2 & 3 to the nearest tenth. 1) Hexagon s = _____ r = ______ a = ______ P = 144 A = ______ 2) Octagon s = 20 r = ______ a = ______ P = ______ A = ______ 3) Pentagon s = 13 r = ______ a = ______ P = ______ A = ______ Find the missing measures for each circle. Leave your answers in terms of . r 4) d C A 13 in 5) 10 m 6) 15 cm 81 mm 2 7) III. Find the exact area of each shaded region, then find the area to the nearest tenth. 8) 9) 10) 11) O A 12 2 6 14 5 3 B page 9 Prisms and Cylinders, Pyramids, Cones, and Spheres (Ch. 12) 1) The radius of a cylinder is 4 m. The lateral area is 192 m2. Find the height of the cylinder. 2) The total surface area of a cube is 2166 squared centimeters. What is the length of an edge of the cube? 3) Find the radius of a right cylinder with a volume of 294 cm3 and a height of 6 cm. 4) Find the height of a right cone whose volume is 924 cm3 and whose base has a radius of 14 cm. Find the surface area and volume of the following figures. ALL UNITS ARE IN FEET. 5) 6) 13 17 10 10 r=8 7) QuickTime™ and a dec ompres sor are needed to s ee this pic ture. page 10