Geomentry Review 3

m Name , Date Name Class GEOMETRY Review #3 - G.SRT.4 SELECTED RESPONSE Select the correct answer. R A a DA FB ^ AE BE ^ ^^^ Given: EFUBC AE AF v 5 DE AE ~ DF AB DA _ AE BE BE ® Q F Class rde of 12. Prove that if a fine parallel td aJriang1e interee( sJbe ttoMasides,IJ ^^ ^ then it divides those sides proportionally. . SX scale factor 3. Find the proportions XQ SY and YR Justify your work. 1. Which of the following proportions could be used as a given to show that ABDDF? D Date CONSTRUCTED RESPONSE 11. In the figure below, U ADE ~ U. with U ABC the image of LI ADI a dilation with scale factor 2. EF EB = Cg> DF AB i Match each statement in the proof below with the correct reason. Note that reasons may be used more than once. Given: U ABC UABC, AP Prove: RU f ~ URS7, AD is a median of RU is a median of URST AB RS j: 2. CD = DB\ TU = US A 3. CS - CP + DB; TS AB _ C8 £ 4 RS TS A Segment Addition Postulate B Substitution Property of Equality C Corresponding sides of similar triangles are proportional D ASA congruence criterion E AA similarity criterion F Definition of median G Division Property of Equality H Corresponding angles of similar triangles are congruent. I SAS congruence criterion = TU + US . . 0 AB CD + DB 5. RS TU + US AB DB + DB DB ~ 6. RS US + US US % 7. ZB = ZS C AD AB ~ 9. RU RS Geometry 8. UABD - URSU J SAS similarity criterion 1 Common Core Assessment Readiness a. How does the altitude CG ct to the altitudej[R? Explain. * - eg 3 b. How does the area of U ABC compare to the area of U AD Explain. r * c. Write a general expression relating the areas of two similar triangles with scale factor k . Geometry 2 Common Core Assessment Readiness - 1 Name. Date Name Class 5. City A is 50 miles north of City B, and City B Is 120 miles east of City C On a G.SRT.5 SELECTED RESPONSE B is 2.5 inches . 3. ABCD is a trapezoid with BCD AD and ZBAD s ZCDA . Which of the following statements can be concluded? 1. A jogging path runs along the river from point C to point £, passing through point A. You want to find the distance DE across a river using indirect measurement. Which congruence criterion can be used to show that LI ABC = U ADE7 a. What is the distance between City B and City C on the map? Cr * d >' / cs ® U AED = U CEB ) UAED - UCEB p © BC = AD ® BEsDE BD - AC © AE = CE 100 ft E B ® sss ) (g) SAS C§) HL 2. In order to measure the height of a large tree, Adrian measures the tree’s shadow and immediately measures the length of his shadow and his height. What is the rJjff in Ihrv Ck b. Use the proportionality of sides of similar triangles to solve for x. Then find the lengths of TU and QS. T U z l Z 0J ^ J 4. Before rock climbing, Michelle wants to know how high she will climb. She places a mirror on the ground and walks backward until she can see the top of the — 1 ' “ X s X 'Vc - \ M * L sdSUWK ^ m a. Show that height of the tree? . JNM c A ? 200 147 ft « 5 B a. Show that U EAB c. Explain how to show thatfj LNM and U LNK are also congruent to U JNM and U JNK . 42.3 ft 4.2 ft &i 31.725 ft 5^ D 42.3 ft CD 47.9 ft ( CAL 0 56.4 ft ) Geometry 300 ft tr b. Show that U JNM and U JNK are right triangles. Adrian .« 8. Andy wants to find the distance across a river. In order to find the distance CD, Andy stands at point D, directly across from point C, and walks 200 feet to the left, placing a marker at a point £ Andy continues walking another 300 feet to point A , and then follows the path to the left, walking until the markers at points E and C line up. Andy marks this location B and measures AB. K /X ~ &M- 'f 6. A plot of land shaped like a rhombus is being turned into a garden. Stakes are * placed at the four comers of the plot, and string aretfied between opposite vertices. Show that the strings divide the plot of land into four congruent right triangles. CONSTRUCTED RESPONSE 0 ASA a. Show UTRU c. What is the distance between City A and City C on the map? D X + 14 Q 13a D 100 ft ? v. / b. What is the actual distance between City A and City C? A TUjfQS. llld Select all correct answers. Select the correct answer. Class 7. In the figure below, . 5«rtV!f 2S c Date 3 Geometry ~ U EDC. b. Use the fact that corresponding sides of similar triangles are proportional to find CD. £.f>clr O» uo * # 4 CornmorrCTcfrrAsi lent Readiness Date >* />L >• * G.SRT.6 sa v Select all correct answers. lo Find the ratio 1. In the figure below, U DEF ~ UGHF. Which statements are true? ' • 5-in-the4iQUre-belawi - ,U Find tan Z/\ and tan ZD. What do you -J -- t zrzfzri: : SC . Class 7. Show that U / BC ^ YZ ’ AS r ~ U Xf| A1ow that O. XY ' notice? SC YZ . B DF E B A £ Date CONSTRUCTED RESPONSE ^^ fTffffrerfigure ^ SELECTEDRESPONSE Name Class Date, Name. 6 5 X c 1125 D Y 5 C 900 D G L 1 F £> F £ J ^ V* ; rMPjz H ® 5 ! V 34 ro re B 0 10 x A J DE EF HF FG flgv FD FG W 6. In the figure, U ABC ~ LI >ADE. 3 ® EF.HF v F ^ DE ” _ ~ GH HF Select the correct answer for each lettered part 4. In the figure below, LI RST ~ L) JKL , JK - 3 , SL = 3, and RT = 10. Decide if each statement is true or false. GH EG Select the correct answer. 2 Use the triangle below to find cos ZV. 8. In the figure below, LJUVW ~ U XYZ. + x W Y U 8 27 s . T u 15 J L Z 6 a. Show that sin U = sin X. R V .t f US ' * y 9 False . Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to tha original content are the responsibility of the instructor Geometry 5 Common Core Assessment Readiness i. Geometry 6 Common Core Assessment Readiness V V / /V & ^ Class Date.. Name Date G.SRT.7 ~2! SL-r=S " \ Match each trigonometric ratio with an equivalent ratio. 5. sin 8“ A sin 45° B sin 65° 6. sin 82° C cos 60° 7. cos 45° D cos 82° 8. cos 35° E sin 90° F sin 55° 9. sin 30° G cos 8° H cos 30° Select the correct answer. 1. If sin 52° « 0.788, what is the approximate value of cos 38°? ® 0.212 _ __ _ _ Name =" t £Ssi ? SELECTED RESPONSE Class Date 11. a. Find sin A in the triangle below. I Class 13. Consider the triangles shown below. 12 £ 4 © 0.384 ® 0.616 © 0.788 2. Given that cos 75° » 0.259, which statement below is also true? C . © sin 75° « 0.259 © sin 15° « 0.966 © cos 15° « 0.259 below. Round your answers to the nearest thousandth. A 3. Given that sin 18° « 0.309, which statement below is also true? 48 © sin 72° « 0.309 © cos 72° « 0.951 B b Write a different trigonometric rat with the same value as sin A. Yr CONSTRUCTED RESPONSE 10. Find the value of each trigonometric ratio © sin 15° « 0.259 16 12. The students in a class were asked t find the value of x in the triangle sho ' The equations two students used to the problem are shown. Which stude equation, if any, results in a correct \ Sf*x?- What is the correct value of x? Round your answer to the nearest thousandth. table? $ cos 72° « 0.309 ( i 4 Select all correct answers. 4. Use the figure shown to determine which of the statements below are true. c 55 >( a. sin A £ A ff V b. cos A sS c. sin 8 sT i c 1 B d. cos 8 (S) sin A = cos B t 1 , 12 2fj % , 4# 7F • * Vv .^ Q 12 cos 55° - — x V' 1 © © cos A = 1 15 A# j 1( sin A - cos A © sin B - cos A /9 © sin A = — S?-. t - cot HS R 8 P . C P* ? Original content Copyright © by Houghton Mifflin Harcourt . Additions and changes to the original content are the responsibility of the Instructor. Geometry r°" 14. In the diagram below, show that sin P = cos -Q and cos P = sin Q. Explain why this is true for any pair of acute angles in a right triangle. 12 Student A: sin 35° = — x 3 f *0 > 2** Student B: i i. 6 co %6 7 Common Core Assessment Readiness * • «7 Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the Instructor. Geometry 8 Common Core Assessment Readiness ~ TJ2 I Date G .SRT.8* Name Class 5. A ladder leans against the wall and reaches-a ntj4,f p4hej Jl.vj:he^ base of the ladder is 6 feet from the wail. ^ ^^ - * SELECTED RESPONSE Select all correct answers. 3. Standing by a lighthouse L, you locate two buoys, J and K. Buoy J is 72 yards north of lighthouse L, buoy Kis 75 yards away from lighthouse L, and buoy K is 21 yards east of buoy J. Which of the following inverse trigonometric ratios could be used to find mZ /.? Select the correct answer. 1. A ramp that is being constructed must be 42 inches long and reach a ledge that is 21 inches tall. Which inverse trigonometric „ ratio could be used to find mZB? A Date Class . ~ jwing due 7. A plane flies with a crosswi ^ should the pilot fly so that the airplane travels due south at 450 mi/h? Draw a sketch that models the situation. Round the speed to the nearest tenth and the angle to the nearest degree. D 24 ft J 21 yd K 21 in J . 72 yd B C E 75 yd fn ® 1 cos " ^ 1 l« J ( ) 1 72 ' 2. City A is 350 miles due south of City B. City C is 500 miles due east of City B. What is the measure of ZC to the nearest degree? tl 500 miles I 21J •“ "(S) CONSTRUCTED RESPONSE 4. Priya has planted a garden shaped like a Shelf - 5* c * CD 44° CD 90° Wall Brace 6. Stefan and Angela are building a ramp with the dimensions shown. To find the height of the ramp, Stefan says they should use the expression 36 sin 29°. Angela says they should use the expression 36 cos 29° c a. To the nearest tenth of a centimeter, how far below the shelf should the brace be attached to the wall? Show your work. /3 & . ___ ^ b. To the nearest degree, what angle does the brace make with the wall? Show your work. ? & ?•« t Tl ^ * c. To the nearest degree, what angle does the brace make with the shelf? Show your work. - / JLv xr ^S * * Whose expression is correct? What error did the other person make? What is the height of the ramp? Round your answer to the nearest tenth. 35° B IH VT ^ 26 cm A C A Geometry Mi b. Explain two ways to find the angle formed by the ladder and the wall using the sides of the triangle or your ah'swer from part a. 350 miles £ 8. A shelf extends perpendicularly 26 cm from a wall. You want to place a 32 cm brace under the shelf, as shown below. 32 cm ' B f a ' ( 21 3 D sin 1 ^/ ! ( ( f 21 72 \ sin-1 21 42 j 6 ft p a. To the nearest degree, what angle does the ladder make with the ground? -f f££ iA a teo /eeA oaUs ff*l 9 Geometry L 10 Common Core Assessment Readiness ' ' I Name Date Class G.SRT. 9(+) Name ~* =TZ2in SELECTED RESPONSE Select the correct answer. TJ!f as5 CONSTRUCTED RESPONSE 3. Write an expression for the area of U XYZ. Then compute the area, rounding to the nearest tenth. 1. Which of the following expressions is equivalent to h , the height of U ABC ? . Z Y 63 cm • ‘ ‘ 1 b C 4- ® c sin B (D b sin C Wt % A -4 5. Consider LIWXY , shown below, in which WX = B and WY = 7. a sin C J 'Y • X 6 Select all correct answers. 2. Which of the following formulas could be used to find the area of U >ABC ? •x I I I 2 * y 120° w -2 - ® ® I I 4 I I I 6 8 I -I 4. If possible, define a sequence of similarity transformations that maps circle A onto circle B If no such sequence exists , explain why not 2. What translation could be used to map point M onto point N? ) . "y X 1 2 CONSTRUCTED RESPONSE . '7 8 OX U>\/ , CM A l.U> b. Use your expression from part b and the values from part a to find the area of LI WXY to the nearest hundredth. A~ k ' L .? . [ —8 I I I I I ft 2 B I H-4 ! -1-M —6 —4 —2v 2 4 6 *x -4 - - -6 (to I -- 6 a. Write an expression for the area of UWXY in terms of the side lengths WY and WX and the measure of ZW , not their values. ! * -8 - - 4 units left, 4 units (§) 4 units right, 4 units up 4 units left, 4 units down (D) 4 units right, 4 units down ' Geometry 11 "V ® x=2 * /L lk VivrT.' T •• I I- > 6 x - 2* - -2 2 (f ) y ®Efc . . 4 - f .?.‘ir r ' -4 -6 - • 8- - . • I.. ra r -- y 4? A - 4- - 30' a h ^ *' y 6 45 cm c — Class == ^ 3. What scale factor could be used to make an image of circle X that is congruent to circle Y? SELECTED RESPONSE Select the correct answer. 1. What is an equation of a line of reflection that maps point X onto point Y? x B . Date G.C.1 Common Core Assessment Readiness Geometry 12 Common Core Assessment Readiness t * Name Class Date -SW esragia SELECTED RESPONSE Select the correct answer. 1. What is the measure of ZACB below? Date G.C.3 G.C.2 Select all correct answers. 3. Choose the expressions below that are equivalent to mZ,40B. A *\\ -- »« J5nra “ ELECTED RESPONSE ^Select the correct answer for each SSSr'SSS lettered part 1 In the diagram below, C is the circumcenter of U XYZ. Classify each statement below. . i *s B C 50° D ® 25° CD 50° CD 1 2 ®i ioo° (mZACB ) Cg) rn ACB ^ (D 150° 2. Which statement below correctly relates ZBDC and ZBAC ? • CD mZDOE CD r(\ZDFE d) 2(mZDFE ) ® m0E — / '0 - j /ti -- Select the correct answer. 2. Which of the following best describes how to find the circumcenter of a triangle? (2) Find the intersection of the three altitudes of the triangle. Cg) Find the intersection of the perpendicular bisectors of the sides of the triangle. CD Find the intersection of the angle bisectors for each angle in the triangle. CD Find the intersection of the three medians of the triangle. 3. You are constructing the inscribed circle for U JKL Choose the best first step below. a CX - CY oTrue ® o False b- C Z - X Y OTrue O False of JK . (D Construct the bisector of ZJ. o Cannot be determined non c. UCXZ is isosceles. oTrue CONSTRUCTED RESPONSE o False 4 Use the diagram to explain why mZADC - 85° . o Cannot be determined d. LI CYZ is equilateral. Construct the altitude from JL to ZK. Cg) Construct the midpoint of KL. CD Construct the perpendicular bisector o Cannot be determined CONSTRUCTED RESPONSE -* Class . oTrue O False o Cannot be determined e- ® ZBDC and ZBAC are XY is a diameter of circle C. complementary. oTrue o False o Cannot be determined i CD ZBDC and ZBAC are . supplementary CD ZBDC and ZBAC are congruent. CD It is impossible to determine a relationship between ZBDC and ZBAC. Geometry Geometry 14 Common Core Assessment Readiness