~ Name·~ Date: _ _ _ _ _ _ __ . ~~-G-e-om-etry-Mi-.d-te_rm_E_x_am_S_tu_d_y Guide Part 1 Chapter 1 Directions: Use the figure to the right for exercises 1-3. 1. N arne two intersecting lines. an SUJ0 S W; II on t pos sIb I e Grt.S LA) Q.f : QT' o...nd ~ v a v 'j) Ts) 2. Name the intersection of planes QRBA and TSRQ. ~ QIZ- OY Q R.. 3. Name three non-collinear points. ansL.uerr J LU; II Vtlr-tj , Ont po5Stbl.e. Qh5UJeJr.' A)P>;o.ncl c D A B Directions: Determine whether the statement is true or false. Explain your reasoning. 4. Two points are always collinear. lir U l!:- / 5. Ray LM and Ray ML are the same ray. F Q 15 .e..) t-UJ 0 ell F-f e r e.. V\ + r ct ~ s· L M 0 ~ M L )' 3rv\-+ 5 =- 4 m-1 0 6. Find the value of m. -3m -- _3y¥~ I 3fT1 -t- 5 4.rry - 10 A 8 I 5=/rYJ-1 . +10 C +1 ' I 5-~ = V'Y) e,onclrumt J sQg~ts J5 CA.+ Gl + 2 .=:-50 m= 7. IfXZ =50, what are XY and YZ? 2Q -t8=50 50 -8 ~=Yl I 1 y ~g l ~ a= Ll ; XY= 21 ;YZ= lCj Directions: Classify each side as scalene, isosceles, or equilateral. 8b. Sa. 8c. Directions: Draw/write answers in the space provided. Use the proper Geometry notations outlined in class. 9b. Draw and label plane ABC 9a. Draw and label _XY" fi •BJ •> <~ ~ X oC. ,_ 10. Draw a plane containing four coplanar points A, B, C, and D, with exactly three collinear points A, B and D ,..... 11. Draw and label JK 12. Draw and label PQ 'I< 1' tj) J ~ p Q 14. A linear pair of angles using the points X, Y ,Z and W with a common vertex of Y. 13 . Draw and label an obtuse angle whose sides are -RQ -RS s and I I0° p_ , " ""7 Q ~~ w LX y E~ 2 =- +o qoo 15. An angle measures 7x -13. Its complement measures 4x + 15. Solve for x and fmd the measure of each angle. · 7 ( <;] ) - I 3-= Lj ·; X - I 3 -t L/ X ·+ I 5-= - - L--J II 'X~ --I l ~p J.i.1_=2 g N:- -), I 3 q0 LJ (_ S> ) + I 5 = L{ l __2__; X- @) 1st Angle = LJ 3° ;2nd Angle = LJ l u Directions: Classify each angle as acute, right, obtuse, or straight. 17. 16. Directions: Use the diagram to the right for exercises 18 and 19. 18. Ifm<MQR=61 andm<MQP=25,m<PQRis (o 1-2.5 =3 to JLOo 0 19. Ifm<NQM = 2x + 8 and m<PQR = x + 22, xis q ·~ LA .Q. n 5 c_on t-1-' 2X+'8=- i? )~ +22 -)( . X=-JL/- 'X-+ . =2.2 Directions: Name a pair of each of the following using the diagram to the right for exercises 20-23. = 21. SuJ?plementary Angles_ O.n .Swe_YJ-W i ll vetvLJ) 20. Complementary Angles <AJJB CAhd<BOC. · 11;. ~ OV\~_r~oss,bl~ anscde.r/ ~'--~-={' <t OF a 11d < F DC 22. Vertical Angles 23 . Linear Pair an_swl_~ W1ll vctr-L-J) QttJtAJ~)·--~· < AOE a r)cl< QIJF £_./?<·--..~ ./-- Qnsvve_r"J" v0d I vtl vvt; DnQ___ F ~ POJJlbl~ answe..~u < £D E a nc!. <ED t:_. one... f-JUS5lv\e. Directions: For exercises 24 and 25, write an equation and fmd the value of x. 24. ' {3x + 11) 0 ~ 6j•" "" 180" 25. 3X+?>l+2-x-lo-=120 ~ -l \ -- 5-x-+'L~ = I g 0 ~-155 x= 31 @ -------- Chapter 2 Directions: Solve the following proofs by filling in the appropriate reason for each statement. 1. Given: B is the midpoint of AC • •B A Prove: AB I •C j Steps 1. B is the midpoint of AC ; ~·--~!? 3. ~~ -~ =BC Reasons I. _____ . _ I I V -€..XI :oe..£.o£.-.m cJRt~--1 2. Given: AD is the bisector of k : A C Prove: m<BAD = m<.CAD 3. Given: Dis in the interior of Steps 1. D is in the interior of <fJJAC 2. m<r:.BAD + m-4:.DA.C =m<.BAC ----~----~~~~~ <.BAC k: A C Prove: m<BAD+m<DAC=m<BAC Srn+Sr'Y\ = b1g Directions: Determine if the conditional is true or false. 4. If an angle is acute, then its measure is 13°. FCl \s .Q_,) 5. If a shape has three sides, then it is a triangle. ! y- U (1 C..,LL+ e., i- C! 0 Lt l c\ -::: I+ -e_. Directions: Name the Property ofEquality (POE) that justifies each statement. Use your algebraic proof notes to help you. 6. 2(x + 4) = 2x + 8 . () D1V1J1 on r roc- D1stvl btA.-h v~ t-'D[~ 8. If7x = 42, then X= 6 0 9. ~TY 0.. V\J1+1 v e JK=MN Po[. 0 +c{ c ~ s yCl H--t r n J Directions: Determine whether each situation uses Inductive Reasoning or Deductive Reasoning to solve. 10. The sun came up this morning. The sun came up the day before that. The sun came up the day before that. Therefore, the sun comes up every day, and will come up tomorrow too. Tnduct,ve i?HUOnln_g 11. Emily checks the weather channel. She sees that there is a warm front in the Gulf of Mexico and cold front in Dallas. The local ra~hows the rain in Huntsville is moving south. Emily decides not to go with Charlie because she thinks it will rain. a . De d Uc& v-e Re_cu on i rlj Directions: Find a counterexample to show that each conjecture is false. 12. The product of any integer and 2 is greater than 2. L. x I= 1_; (2 15 e~uCLI 13. The city of Portland is in Oregon. +-o 1, not- g~'eo.__t-e_ . . ) 1 Pov+tGLncl, mOc..lnL IS ctiJo I J 0 lA + J I ct ~ of Dvtg D n ' 0.. c_;f-:J QncL r+ Directions: Rewrite each sentence as a conditional statement. inv~rse, and contrapositive of the given conditional. sw1f~~+ ate 16. Conditional: If a figure is a square, then it has fo~ides. Directions: Write the converse, Swt-kh n ~afe Directions: Solve the following proofs by filling in the appropriate reason for each statement. 17. = Given: ~s 12.. Prove: X :::: 13 •-- ~±1 __ .. . __ ].g_____. 0 S F1 41 Statements QS=42 QR + RS = QS Sm-t Srn-= bl (x + 3) + 2x = 42 3x+ 3 = 42 3x=39 X=13 -¥+12~~:~13 18. Given: 3x + 12 = 8x- 18 Work: -Prove: x= 6 5 X-I ~ +J & -t 118 2Q ~-6~- - ~ ll_=:: 5§ ~ Reasons 21. Find m<BED. 3(18)+20= 7 5(i8)-lw= 22. Find m<AEB. y= !55 4 74- m<AEC = f LJ- 0 m<AEB=

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