Chapter 5 Test, Form 2A
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1 - - - NME DTE PEROD hpter 5 Test, orm 2 ORE Write the letter for the correct nswer in the blnk t the right of ech question. or Questions 1 4, refer the figure. 1. Nme n ngle biseci. D K GL JM DHJ Nme medin. M GGL 3. Nme n ltitude. K GL 4. Nme perpendiculisecr. M GGL HJM JEt] 2. JM DHJ 3. HJM JHJ 4. J z D - - D D - ) or Questions 5 7, refer the figure determine which is true sttement for the given informtion. 5. YW is n ngle bisecr. LYWZ is right ngle. X1V = WZ LXYW LZYW D XY = ZY 6. YVis n ltitude. LYWZ is right ngle. G ZXYW LZYW 7. YWismedin. ZYWZ is right ngle. ZXYWZZYW 8. Nme the longest side of Ls.. G H XW=WZ J xy=zy HG XW=WZ XY=ZY J cnnot tell 9. Nme the ngle with gretest mesure in L.DE. LD Z ZE cnnot tell E% 1. Which theorem compres the sides of the sme tringle? Hinge Theorem H Exterior ngle nequlity Theorem G onverse of the Hinge Theorem J Tringle nequlity Theorem Tish wnts plnt grden in the widest corner of her tringulr bckyrd. The bckyrd is bordered by the bck of the house tht is 5 feet long, fence tht is 27 feet long, nd fence tht is 35 feet long. Which corner hs the widest mesure? corner between fences nd ll three corners hve the sme mestire corner between the bck of the house nd fence D corner between the bck of the house nd fence X c hpter 5 51 Glencoe Geometry
2 NME DTE PEROD 5 hpter 5 Test, orm 2 (coiztinued) 12. ind the possible vlues for rnli. 9>rnLi>74 H <mzl<74 G 18 > mll> 74 J mli = G 13. ind the vlue of x. 9 li 27 D32 x+ 7 x+ 14. Which is nother nme for n indirect proof? proof by deduction H proof by inverse G proof by converse J proof by contrdiction 14. J 15. hoose the ssumption you would mke strt n indirect proof of x < 2. x>2 x2 x=2 D x hoose the ssumption you would mke strt n indirect proof. Given: Li is n exterior ngle of /3. Prove: mll = ml + ml Li is not n exterior ngle of. G Li is n interior ngle of L. H mzl ml + rnl J mll=ml 16. H 17. Which of the following sets of numbers cn be the lengths of the sides of tringle? 6, 6, 12 6, 7, 13 V, Vi D 2.6, 8.1, D 18. Wht is the reltionship between the lengths of Q nd R? Q$=R H Q$>R$ G Q <R J cnnot tell 19. Wht is the reltionship between the lengths of D nd D? D<D D=D D > D D cnnot tell 2. Wht is the reltionship between the mesures of Li nd Z2? mll=rnl2 H rnli > rnl2 G mzl<ml2 J cnnot tell R T 83 8 H H D D D 3 D D, D 5 3 D D, onus YW bisects LKYZ in XYZ. Point W is on XZ. fmlxyw = 2x + 18 nd mlzyw = x2 5x, find the possible vlue(s) of x. : 9, 2 hpter 5 52 Glencoe Geometry
3 NME DTE PEROD 5 hpter 5 Test, orm 1 ORE Write the letter for the correct nswer in the blnk t the right of ech question. or Questions 1 4, refer the figure t the right. G 1. Nme n ltitude. E DE D D 2. Nme perpendiculr bisecr. DE G HG J Nme n ngle bisecr. DE G D 3. H D 4. Nme medin. DE G HG - J or Questions 5 7, refer the figure determine which is true sttement for the given informtion. D 5. is medin. rnld=9 =D Z LD D L LD 5. g 6. is n ngle bisecr. mld=9 G LLD H =D J LLD 6. G 7. is n ltitude. mld =9 Z LD 8. Nme the longest side of L.DE. DE HD G E J cnnot tell Which ngle in hs the etest mesure? L L P cnnot tell Which theorem compres two sides nd the included ngle of two tringles? Hinge Theorem G onverse of the Hinge Theorem H Exterior ngle nequlity Theorem J Tringle nequlity Theorem Which ssumption would you mke indirectly prove x> 5? x<5 x5 x=5 P x>5 11. H hpter 5 49 Glencoe Geometry
4 NME DTE PEROD 5 hpter5test, orm 1 (continued) 12. ind the possible vlues for mli. 18>rnZi>62 H <mll<62 G 9 > mli > 62 J mzl = ind the vlue of x. 5 cio M\ 7 15 x W/N 14. f D is the circumcenter of /. nd D = 6, find RD. t 119 G6 J hoose the ssumption you would mke strt n indirect proof of x > 3. x<3 x3 x3 D x=3 15. G 16. hoose the ssumption you would mke strt n indirect proof. Given: Prove: Li nd L2 re not supplementry. Wb H L1L2 G Li nd L2 re supplementry. J Li nd L2 re complementry Which of the following sets of numbers cn be the lengths of the sides of tringle? 12, 9, 4 1, 2, 3 5, 5, 1 D \/, V, v i is medin of LE. f E = 15. find G 7.5 J 3 D E 18. G G or Questions 19 nd 2, refer the figures. 19. Given: D, DE,,nL > rnld Which cn be concluded by the Hinge Theorem? L\ DE <E D =E D >E E/ \ 19. D 2. Given: DE, E, <D Which cn be concluded by the onverse of the Hinge Theorem? ml <rnle H ml = mle G ml > mle J LED 2. onus Q is medin of PQR with point $ on R. f P = x2 3x nd R = 2x + 6, find the possible vlue(s) of x. : 6 1 hpter 5 5 Glencoe Geometry
5 - - NME DTE PEROD r..s2i;tjii:est, orm 2 ORE Write the letter for the correct nswer in the blnk t the right of ech question. or Questions 1 4, refer the figure. 1. Nme medin. RW V QT DR 2. Nme n ngle bisecr. RW GV HQT JR Nme perpendiculr bisecr. RW V QT DR 4. Nme n ltitude. RW GR HQT JR or Questions 5 7, refer the figure determine which is true sttement for the given informtion. 5. G is n ltitude. ZDG is right ngle. DG = GE D = E ZDG EG G D 5 -. >, z, (!J 6. G is medin. LDG is right ngle. G D=Ef 7. G is n ngle bisecr. ZDG is right ngle. D=E 8. Nme the longest side of. G H DG=GE J LDG LEG DG=GE D LDG LEG H J cnnot tell 9. Nme the ngle with the gretest mesure in t.gh. G L H LH cnnot tell 62 7O H 9.c, > 1. Two sides of tringle re congruent two sides of nother tringle nd the included ngle in the first tringle hs greter mesure thn the included ngle in the second tringle. These re the ssumptions of which theorem? Hinge Theorem H Exterior ngle nequlity Theorem G onverse of the Hinge Theorem J Tringle nequlity Theorem 1. hpter 5 53 Glencoe Geometry
6 3, NME DTE PEROD 5 hpter 5 lest, orm rrie, Mri nd Nyl re friends tht Nyl live close one nother. Which two friends hve the shortest distnce between them? (2x + 7) Mri nd Nyl rrie nd Mri rrie nd Nyl D rrie (5x + 5) (5x + ll three live equl distnces from ech other ind the possible vlues for mli. mli=i24 H9>mLl> G <mll <56 J 18 > rnll > 56 R ind T. $ x 1 18 D 24 x+6 T 14. Which of the following is the lst step in n indirect proof? show the ssumption true H show the conclusion flse G show the ssumption flse J contrdict the conclusion 14. G 15. hoose the ssumption you would mke strt n indirect proof of x 1. x>1 x=1 x<1 Dx1 16. hoose the ssumption you would mke strt this indirect proof. Given: bisects LD. Prove: Z LD does not bisect LD. H is medin. G D is isosceles. J Z LD Which of the following sets of numbers cn be the lengths of the sides of tringle? 12, 9, 2 11, 12, 23 2, 3, 4 V, \1, /i Wht is the reltionship between the lengths of YW nd YX? YW=YX H YW>YX Z G YW < YX J cnnot tell x w 18. G 19. Wht is the reltionship between the lengths of DG nd G? DG>G DG=G DG < G cnnot tell 19. E&N 2. Wht is the reltionship between the mesures of Li nd L2? rnll = ml2 H mzl > ml2 1 N K G rnll <ml2 J cnnot tell 2. H Mri onus HJ is n ltitude of GH with point J on fmlgjh=5x+3,gh=3x+4,h=5x 3, J = 4x nd GJ = x + 6, find the perimeter of GH. : M 16 hpter 5 54 Glencoe Geometry
7 NME DTE PEROD hpter 5 lest, orm 2 ORE 1. Nme n ngle bisecr The perimeter of R D is 44. ind the vlue of x. Then describe the reltionship between nd D. D 2. x = 8; is thei.. bisecr of D. 3. f point E is the centroid of, D = 12,E = 7, ndg = 15, find ED The vertices of LXYZ re X( 2, 6), Y(4, 1), nd Z(14, 6). find the coordintes of the centroid of LXYZ f O is n ngle bisecr of ZMON, find the vlue of x. ((X P 2, 6. biker will jump over rmp, where x nd z re mesured in feet. Write n inequlity relting x nd z. (z+3)7q. 6. 2(z + 3) > - 7. List the ngles of LGH in order from smllest lrgest mesure. 21n. ci, ch, cg - 8. List the sides of PQR in order from shortest longest. 45\ PQ, PR, QR 9. ind the shortest segment. w 1. Write the ssumption you would mke strt n indirect proof of the sttement. f 16 is fcr of n, then 4 is fcr of n is not fcr of n. X Write the ssumption you would mke strt n indirect proof of the sttement. f R is n ltitude of equilterl tringle, then R is medin. 11. is not medin. hpter 5 55 Glencoe Geometry
8 NME DTE PEROD :: 5 Test, orm 2 (continued) 12. Write the ssumption you would mke proof for the following. strt n indirect Given:XY Prove: YZ YWbisects ZXYZ. LX LZ 12. LXLZ 13. The mesures of two sides of tringle re 1 meters nd 23 meters. f the mesure of the third side is x meters, find the rnge for the vlue of x is medin of PTQ. f Q = 6, find TQ. // c / / ft \ N m<x<33m f bisects, find the vlue of x Write n inequlity compre E nd GH. H 6 E 2O 16. E<GH 17. Write n inequlity compre mzl nd ml2. or Questions 18 2, complete the proof below supplying the missing informtion for ech corresponding loction. Given:D = nd > D Prove: mld > mld 5 ft 12 t by ft 17. mll > ml2 m Proof: ttements Resons, D 1.D=nd>D D DD 4. mzd > mld 1. Given 2. (Question 18) (Question 19) 19. Definition of segments Reflexive Prop. (Question 2) 2. onverse of Hinge Th. D D ( onus Write n eqution in slope-intercept form for the ltitude. (2. 2b) : = c 1,4( ) (2c, ) hpter 5 56 Glencoc Geometry
9 NME DTE PEROD 5 ffhpter5test, orm 2D ORE 1. Nme perpendiculr bisecr. G The perimeter ofrq is 34. ind the vlue of x. Then describe the reltionship between nd Q. R 1 4x 1 2. Q) 2x 3 x=5; Risthe..L bisecr of PQ. 3. f point N is the centroid of ZHJ, M = 18, KW = 4, nd HL = 15, find JN. H The vertices of L,.DE re D(4, 12), E(14, 6), nd ( 6, 2). ind the coordintes of the circumcenter of LDE. T (5x 1) 5. f R is n ltitude for /RT, find R the vluex rubber doorsp hs side mesuring 7z nd height mesuring x 5. Write n inequlity relting x nd z. l5o 6. 7z > x 5 -c. > 7. List the ngles of TV in order from smllest lrgest mesure. 8. List the sides of LGH in order from shortest longest. 9. Nme the longest segment. /N 8. H,GH,G H \G L M 9. LT,LV,L.,. 1. Write the ssumption you would mke strt n indirect proof of the sttement. f n is n even number, then n2 is n even number. K,.2 is not n even 1. number. 11. Write the ssumption you would mke strt n indirect proof of the sttement. f D is n ngle bisecr of equilterl tringle DO, then D is n ltitude. 11. b is not n ltitude. hpter 5 57 Glencoe Geometry
10 NME DTE PEROD (5 hpter 5 lest, orm 2D (continued) 12. Write the ssumption you would mke proof for the following. Given: Vis not the midpoint of PQ; V PQ. Prove: <P strt n indirect PQ 13. The mesures of two sides of tringle re 14 feet nd 29 feet. f the mesure of the third side is x feet, find the rnge for the vlue of x. 14. D is medin of E. f D = 8, find DE. 15. f bisects /XYZ, find the vlue of x. Y DE 3x 2 w 2x V±PQ 15ft<x<43ft Write n inequlity relting mz1 7 nd rnl m < m2 17. Write n inequlity relting c nd ED <ED or Questions proof below 18 2, by complete the supplying the missing informtion for ech corresponding loction. Given: K is the midpoint of. mzmk <mzmk Prove: M Proof: <M ttements Resons E M K D D G) D D D 1. K is the midpoint of. mzmk < mlmk4 2. KK 3. MK 4.M3 MK <M 1. Given 2. (Question 1$) 3. (Question 19) 4. (Question 2) Midpoint Theorem Reflexive Prop. HingeTh. D D D D onus Write n eqution in slope-intercept form for the perpendiculr bisecr of E. c) : x = O(. ) Et ) X hpter 5 58 Glencoe Geometry
11 NME DTE PEROD 5 hpter 5 lest, orm 3 ORE 1. f point G is the centroid of L, R = 24, DG = 5, nd G 14, D E findd. 2. The vertices of EG re E(2, 4), (1O, 6), nd G( 4, 8). ind the coordintes of the orthocenter of LEG ( f JL is medin for LJK, find the vlue of x. K 3x+1O L 2x Write compound inequlity for the possible mesures of LL. L M >mLL>O 5. List the ngles of LGH in order from G smllest lrgest mesure. 5 LH,Z,LG 6. List the sides of QR in order from Q shortest longest. so 6. QR, PQ, PR ) ) 7. Nme the shortest nd the lonoest X segments. W_/\\ R 72y shortest: W; longest: VW V Write the ssumption you would mke begin n indirect proof of the sttement. f 2x + 6 = 12, then x = Determine whether 8, 4, nd 2 cn be the lengths of the sides of tringle. Write yes or no. Explin. x#3 9- no;2+4<8-1. Write the ssumption you would mke begin n indirect proof of the sttement. The three ngle bisecrs of tringle re concurrent. in The L bisecrs re not concurrent. 11. Write nd solve n inequlity for x. 112x 31) x 31 > 3x x>3 4; hpter 5 59 Glencoe Geometry
12 L5 hpter 5 lest, orm 3 contiiued) NME DTE PEROD 12. f H is medin of LEG find the perimeter of /EG. 2x+23H 7x Write the ssumption you would mke n indirect proof for the following. Given: DR nd D Z strt Prove: >E 13. LLE 14. The mesures of two sides of tringle re 24 inches nd 29 inches. f the mesure of the third side is x inches, find the rnge for the vlue of x in. < x < 53 in. 15. YW is the perpendiculr bisecr of ZT. f TW = 3, YW 8, ndxz = 12. indxy z w 16. Write nd solve n inequlity for the vlue of x. 8 3x+1O x x + 1 > x + 2; x>5 or Questions supplying the missing informtion for ech corresponding loction. 17 2, complete the proof below Given:XW=YZ,XK>WK,ndKZ>KY Prove: mlxwz > mlyzwk Proof: ttements Resons 1.XW=YZ,XK> nd KZ>KY 2.XW 3.XZ> YZ WY 4.WZWZ WK, 5. mzxwz > mzyzw onus 1. Given (Question (Question (Question (Question Write n eqution in slope-intercept form for the line contining the medin DE. 17) 1$) 19) 2) z y y by E(2c. 2c W Def. of segments 17. ddition Prop. of 1 nequlity Reflexive Prop. 2. onverse of Hinge Th. : d 2d c 2 c 2 c 6 ) ) G). -.4 ) 3 ) OD(O, ) (2 ) hpter 5 6 Glencoe Geometry
13 vlue of x. possible mesures of ZL. NME DTE PEROD [5/hpter 5 lest, orm 3 ORE 1. f point G is the centroid of L43, R = 24, DG 5, nd G = 14, E findd. 2. The vertices of /EG re Et2, 4), (1O, 6), nd G( 4, 8). ind the coordintes of the orthocenter of EG. 3. f JL is medin for 7JK, find the (38 32 il x+1O L 2x Write compound inequlity for the M >mLL>O 5. List the ngles of /GH in order from G smllest lrgest mesure. 5. LH,L,LG 6. List the sides of PQR in order from Q shortest longest. 8O 6. QR, PQ, PR, ), 7. Nme the shortest nd the longest segments. W\ \72y V 7. shortest: i7v longest: VW - -., > 8. Write the ssumption you would mke begin n indirect proof of the sttement. f 2x + 6 = 12, then x = x#3,, ), 9. Determine whether 8, 4, nd 2 cn be the lengths of the sides of tringle. Write yes or no. Explin. 1. Write the ssumption you would mke begin n indirect proof of the sttement. The three ngle bisecrs of tringte re concurrent. 11. Write nd solve n inequlity for x. 9 no;2+4<8 The L bisecrs re not concurrent. (3x (12x 31) x 37 >3x 4; x>3 hpter 5 59 Glencoe Geometry
14 2x+23H 7x 2 perimeter of LEG. 12. f H is medin of LEG, find the / hpter 5 Test, form 3 (continued.) medin DE. : 2 form for the line contining the 5. mlxwz> mlyzw 4.WZWZ 3.XZ> WY 2.XW YZ nd KZ>XY x>5 16. Write nd solve n inequlity for f TW = 3, YW 8, ndxz = 12. indxy. 15. V is the perpendiculr bisecr of ZT. rnge for the vlue of x The mesures of two sides of tringle re 24 inches nd 29 inches. f the mesure of the third side is x inches, find the Prove: L LE >E 13. LE Given: R DR nd D strt n indirect proof for the following. 13. Write the ssumption you would mke NME DTE PEROD R -i-1fl 3x + 1 > x + 2; XW = YZ, XK> WK, 1. Given 5. (Question 2) E(2c.2th %_% d 2d ) (2 ) hpter 5 6 Glencoe Geometry onus Write n eqution in slope-intercept 2. onverse of Hinge Th. 4. (Question 19) 2. (Question 17) 3. (Question 18) 17. Def. of segments ddition Prop. of 18. nequlity 19. Reflexive Prop. ttements Resons Proof: z w Prove: mlxwz > mlyzw K Given: XW = YZ, XK> WK, nd KZ > KY y loction. supplying the missing informtion for ech corresponding or Questions 17 2, complete the proof below by the vlue of x. 16. z -- -\ T in. < x < 53 in. D D D D, D, D 3 D D D D, D 3 3 V D D D D,
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