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Geometry Name___________________________________ Mixed Review Date________________ Block____ ©m l2c0j1W47 DKAuvtNa8 RSQoKfetAwHaUrket mLaLYCN.i N HA8lnl8 5rhipgqhHt0sS 7rje7sVerrdvHeQda.7 Find the measure of the angle indicated in bold. 1) Given: p: It is a B day q: It is a snow day r: We have math 2) 9 + 9x Convert the following statement to symbolic form: If it is a B day and it's not a snow day then we have math. 10 x Find the value of x that makes lines u and v parallel. Find the coordinates of the vertices of each figure after the given transformation. 3) 4) rotation 90° counterclockwise about the origin y 75° u v x + 80 x F S Q R Find the distance between each pair of points. Answer in simplest radical form and to the nearest tenth. 5) Find the other endpoint of the line segment with the given endpoint and midpoint. 6) Endpoint: (8, 10), midpoint: (−3, −4) (−7, 7), (−5, 3) State if the three numbers can be the measures of the sides of a triangle. Two sides of a triangle have the following measures. Find the range of possible measures for the third side. 7) 3, 9, 6 ©1 K2X0I1j4Q wKtugtIal bSMoff2towfaQrHed 5LpLtCO.G e 3AIlJlC arki8gnhxtgs1 drle7sheEr9vie8d1.i w 9MQaKdYe9 OwoiVtshm gIFnyfxiSnYiUtteJ SGyeeoXm3eMt2rnym.9 8) 10, 12 -1- Worksheet by Kuta Software LLC State what additional information is required in order to know that the triangles are congruent for the reason given. Solve for x. 9) 5 10) SSS 7 4 T S 2x − 4 K R Find the measure of the angle indicated. Order the sides of each triangle from shortest to longest. 11) Find m G. 12) D G C 30° 100° H 11 x + 4 7 x + 8 50° E 120° F U Find the value of x. Solve for x. 13) m 2 = x + 42 14) G x + 27 T 75° x + 17 2 I Solve for x. The triangles in each pair are similar. 15) C D H U Find the missing length indicated. Leave your answer in simplest radical form. 16) x 18 2x − 1 16 T 12 77 V 66 U ©l x2F0j1i4e qKmuitUav GS7ovfBt8wIaSr6ew oLLLBC6.C 5 pA9ldlQ GrYi5g1hktusf 4rzeosee8r1vieTdy.V 8 GMYacdPe3 uwWixtzh7 0I5ntfaiXnli8tcel DGAeJoMmjeXt6ryyC.u -2- Worksheet by Kuta Software LLC Find the missing side lengths. Leave your answers as radicals in simplest form. 17) 18) x y 30° 45° y 5 x Find the missing side. Round to the nearest tenth. 19) 53° 8 Find the measure of the indicated angle to the nearest degree. 20) 18 14 x ? 20 Find the value of the trigonometric ratio. 21) cos C B 36 A Find the measure of one interior angle in the polygon. Round your answer to the nearest tenth if necessary. 22) regular nonagon 27 45 C Find the measure of one exterior angle in the polygon. Round your answer to the nearest tenth if necessary. Solve for x. Each figure is a parallelogram. 24) MW = 9 YW = 2 x − 2 W X 23) regular 11-gon M Y Z Solve for x. Find the length of the darkened arc in terms of π . 25) 26) E 58° 6 ft 135° D 9x + 8 C ©w i270F174N wKXuRtva7 ESaojfTtZwWaHrOe0 KLsLfCt.T 9 SAWlxl4 PrSiGgqhEtcsH frIeWsoecrgvDe2dF.c D 8M7aQdQel Bwxistwhl IILnLfMinnlidtxeG ZGJe7oamKewtUroys.x -3- Worksheet by Kuta Software LLC Solve for x. Assume that lines which appear tangent are tangent. Find the segment length indicated. Assume that lines which appear to be tangent are tangent. 27) 28) x 14.4 9 ? 19 8 19.4 Find the surface area of the figure. Round your answers to the nearest hundredth, if necessary. Find the volume of the figure. Round your answers to the nearest hundredth, if necessary. 29) 30) 10 m 6.9 km 7 km 7 km 8m Write the equation of the circle. 31) Center: (−10, 3) Radius: 8 32) Find the center and radius of the circle described by the equation: 0 = x 2 + y 2 + 10 x + 7 Write the slope-intercept form of the equation of the line described. 1 33) through: (−4, 5), parallel to y = − x − 4 2 1 34) through: (−2, −1), perp. to y = − x + 1 2 Solve for x. Assume that lines which appear tangent are tangent. Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent. 35) 36) 120° K R 7x + 1 4x + 1 ? S 6 10 ©H L2d041r4q UKiuwtnaX VS1oXfGt6wHaTrDe3 lL7LoCh.k T vAtlzlS brAijgyhStmso VrBetsgeorkvieSdH.C z BMdamd0eB lwSixtvh5 fIPn8fZiwnFiAtMeD YGfedovmjeytRrgyz.B U 40° T -4- Worksheet by Kuta Software LLC Geometry Name___________________________________ Mixed Review Date________________ Block____ ©S f2P0w1Y4N 4KYuJtEav 9Sco8fDtBw0a5ree2 tLbLSCw.w I JAjl1lW srfixgkhatPsH 3rUensVe9rkvdekdg.M Find the measure of the angle indicated in bold. 1) Given: p: It is a B day q: It is a snow day r: We have math 2) 9 + 9x Convert the following statement to symbolic form: If it is a B day and it's not a snow day then we have math. (p^~q)->r 10 x 90° Find the value of x that makes lines u and v parallel. Find the coordinates of the vertices of each figure after the given transformation. 3) 4) rotation 90° counterclockwise about the origin y 75° u v x + 80 x −5 F S Q R R'(4, −2), S'(2, −3), F'(2, −1), Q'(3, 0) Find the distance between each pair of points. Answer in simplest radical form and to the nearest tenth. 5) Find the other endpoint of the line segment with the given endpoint and midpoint. 6) Endpoint: (8, 10), midpoint: (−3, −4) (−7, 7), (−5, 3) (−14, −18) 2 5, 4.5 State if the three numbers can be the measures of the sides of a triangle. 7) 3, 9, 6 No ©t z2E0Y1U4w GKBuJtBaJ 3SaonfYt3wwaPrSeY kL0LGCL.7 P oAulMln zrqiKgchZt9sb wr2e4s2eOravDeedb.5 h DM6aldFei iwBiftlhU gIjnTfFiqn2iYtleJ aG1eCommQevtsrfyc.5 Two sides of a triangle have the following measures. Find the range of possible measures for the third side. 8) 10, 12 2 < x < 22 -1- Worksheet by Kuta Software LLC State what additional information is required in order to know that the triangles are congruent for the reason given. Solve for x. 9) 5 10) SSS 7 4 T S 2x − 4 7 K R ST ≅ KR Find the measure of the angle indicated. Order the sides of each triangle from shortest to longest. 11) Find m G. 12) D G C 30° 100° H 11 x + 4 7 x + 8 50° E EC , DC, ED 120° F U 70° Find the value of x. Solve for x. 13) m 2 = x + 42 14) G x + 27 T 75° x + 17 2 I −12 −7 Solve for x. The triangles in each pair are similar. 15) H U C D Find the missing length indicated. Leave your answer in simplest radical form. 16) x 18 2x − 1 16 T 12 77 66 9 V U 11 ©v c2m0J1h48 GKkuAtKa5 2SCoKfjtSwsa8r2el yLHLZCb.c o EA2l8ly 0rSiWgThltNsv ArEepsKeMrGv8e0dr.0 a AMxaTdoeN 2wzi4tSh2 6I2nufOifnJiVtFeZ iGXeHozmIeNtsrDyl.2 -2- Worksheet by Kuta Software LLC Find the missing side lengths. Leave your answers as radicals in simplest form. 5 3 5 17) x= , y= 18) x y 2 2 30° 45° y 5 x 8 x = 4 2, y = 4 2 Find the missing side. Round to the nearest tenth. 19) 53° Find the measure of the indicated angle to the nearest degree. 20) 18 14 x ? 20 26° 17.5 Find the value of the trigonometric ratio. 3 21) cos C 5 B 36 A 22) regular nonagon 140° 27 45 Find the measure of one interior angle in the polygon. Round your answer to the nearest tenth if necessary. C Find the measure of one exterior angle in the polygon. Round your answer to the nearest tenth if necessary. Solve for x. Each figure is a parallelogram. 24) MW = 9 YW = 2 x − 2 W X 23) regular 11-gon M 32.7° Y Z 10 Find the length of the darkened arc in terms of π . 9π 26) ft 2 Solve for x. 25) E 58° 6 ft 135° D 9x + 8 C 12 ©B a2m0j114e QKuuUtPa7 uS9offatjw7axr2ea sL4LsCQ.Z x aAElwlk zrJiOgEhHtVsF NrMezsEeor6vmeWdF.j 4 9MUaFd7e6 cwDiOtDhc oIZnBf2ibn1iltMeK sG5eyoLmqeHtsrwyu.p -3- Worksheet by Kuta Software LLC Solve for x. Assume that lines which appear tangent are tangent. Find the segment length indicated. Assume that lines which appear to be tangent are tangent. 27) 28) x 14.4 9 ? 19 8 19.4 15 13 Find the surface area of the figure. Round your answers to the nearest hundredth, if necessary. Find the volume of the figure. Round your answers to the nearest hundredth, if necessary. 29) 30) 10 m 6.9 km 7 km 7 km 8m 167.55 m³ 145.6 km² Write the equation of the circle. 31) Center: (−10, 3) Radius: 8 ( x + 10) 2 + ( y − 3) 2 = 64 32) Find the center and radius of the circle described by the equation: 0 = x 2 + y 2 + 10 x + 7 center (−5, 0); radius 3 2 Write the slope-intercept form of the equation of the line described. 1 1 1 3 through: (−2, −1), perp. to y = − x + 1 33) through: (−4, 5), parallel to y = − x − 4 y = − x + 34) 2 2 2 y = 2x + 3 Solve for x. Assume that lines which appear tangent are tangent. Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent. 35) 36) 120° K R 7x + 1 4x + 1 ? S 6 10 U 40° 2 ©L m2I0K114h TKmuMtaau SSjojfdtHwPa7rPeB wLhLECG.S U oAJlNlI DrzijgIh7tmsC PrPeksAeUrVvceadD.n K 5MKa0d5eo QwWigtohO gItnJfJiInhiPtkeC 7Guetotm1ectJr7yG.b T 40° -4- Worksheet by Kuta Software LLC