MCQ For Geometry. Similarity

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Hector Hicks
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1 MQ For Gomtry Similrity. E F EA FB AE A EB B t G ) ) ) In right ngl tringl, if BD A thn BD AD D n Th ro of r of two imilr tringl i l to r of th ro of thir orrpg i. A ( ) B A A ( ) Q P l Propr of imilr tringl If DEF; thn DEF If DEF n DEF thn r Angl itor proprty t p If lin prlll to i of tringl intrt th othr i in two int point; thn th lin ivi tho i in propor. h A h A h Stnr Angl : o of th r of two tringl i l to th ro of th prout of thir n orrpg hight. Appollou Thorm In if AD i min; thn, + A AD + BD

2 MQ' MLTIPLE HOIE QESTIONS (MQ') (Eh rri mrk). Th ro of th r of two tringl with l n l hight i Th ro of th r of two tringl with th omm i :. Hight of th lrgr tringl i 9 m; thn th orrpg hight of th mllr tringl i If lin ivi ny two i of tringl in th m ro; thn th lin i... to th thir i.. prlll prpulr intrng grunt Th lin joing th mipoint of ny two i of tringl i... of th thir i B AD D A AD A Th i of r who igl i m i In whih typ of tringl i th r of hypotnu l to th um of th r of th rming two i. ight ngl tringl rtr In th right ngl tringl, 90º, g BD hypotnu A; thn BD i l to thr fourth. twi hlf In lin l i B, BP, AQ ; thn th v of Q i.... Eiltrl tringl Otu ngl tringl Aut ngl tringl If th ngl of tringl r 0º, 0º, 90º; thn th i oppoit to whih ngl i hlf th hypotnu. 0. 0º 90º 0º º Amg th following group whih of thm form th i of right ngl tringl.. 9,0,,, 0,0,0 0,,7 Th lngth of th ltu of n iltrl tringl who i i m i.... Similrity

3 GEOMETY S.S... Two tringl hv th m r. If thir r in th ro : th ro of thir hight will..... : : : DEF, DE, B EF?..... : A lin intrt i n A of in point P n rpvly. If In th joing figur + B? AD + A BD + AD thn A( )... A( ). BD + A BD + A From th inform givn in th figur, tt th tt y whih th tringl D n BD r imilr?... Hypotnui S.A.A In th joing figur, if XZ 0, thn fin th v of YD In, P i th point g uh tht In, ry PM it QP, QM. If 9, P, Q 0, fin M º. A( ) 7 9 thn. A( )? 9. º If n 0º. 70º 00 S.A.S A.S.A. 0º, thn?.... A n PB 00 0 In n ºº90º tringl, if prpulr i i, thn th r of tringl i...(ut) 7 Similrity 8

4 MQ' Anwr. (). (). () 7. () A [Givn] PB vr of Bi Proporlity Thorm. vr of Bi Proporlity Thorm hlf Bi proporlity Thorm. Proprty of gomtri mn AD D Pythgor thorm x + x x 9. () 0º0º90º Thorm, 0º 0. () vr of th Pythgor Thorm, 9,0, Pythgor Thorm ight ngl tringl. 0º0º90º Thorm. () A [Tringl hving l r] A A h A h (). 7. () DEF B DE EF EF EF A( ) A( ) (7) (7), 9 () [orrpg ngl tt] In QM [By ngl itor thorm] P M 9 QM M By ompno, h h h h (). () [Thorm r of imilr tringl] () P B [vr of B.P.T] 0º [orrpg ngl tt] 0º AQ Q Q Q 0 PB x x 8. In () () i... h h 9 h 7. () A A. EF Tringl with l n l hight r l in r. (). () QM 0, M M 0 M n hv omm vrtx n thir li th m lin. Thir hight r l A P A( ) A( ) B [Tringl hving l hight] [...t] Similrity A( ) A( ) A( ) A( )

5 GEOMETY S.S.. By Appollou thorm, 9. () + B BD + AD S.A.S tt AD D. BD BD 0. () YD 0 8 q.ut In n ºº90º tringl prpulr i r grunt D BD[S.A.S] () XZ YD ADB BD 90º YD YD In right ngl tringl min () n hight r l. A th hypotnou i of th hypotnu h 8. 7 A 8 q. ut. m 8 m 0 m m ngl i pln tringl. 8. 0º º 0º 90º 8 7: :8 : In 0º0º90º tringl th i oppoit A B P m th hypotnu 90º º 0º 0º If th ngl of tringl r ºº90º; thn h of th prpulr i i... m th hypotnu. Similrity In th following figur lin l lin m lin n thn In, i min. If 7, + A 0; thn B.... 9: In th joing figur XYZ i tringl Y 90º, Z º n X + 0º; thn th v of i.... to whih ngl i If th two tringl r imilr; thn th orrpg... r in propor. If th r of two imilr tringl r 8m n 9 m rpvly; thn th ro of thir orrpg hight i In th joing figur MNK i right ngl tringl N 90º, M 0º, MN m; thn MK..... Prolm For Pr i l to.... B B Q Q

6 B Q Appollou Thorm imnn' Thorm In th joing fig., AE, BE E, DE, Thn E ~ DE y th... tt. ASA SSS SAS SAA Thl' Thorm Grfil' Thorm In, g S i th itor of. PS 8, SQ, P 0; thn Q Anwr 9 0. P..8. D x In th joing figur, lin i EF PE 7., DQ.8, QF.; thn DP.... Bi proporlity thorm i lo known MQ'. 0. Th primtr of n iol right tringl with h of it grunt i 7 m i Similrity

Planar Upward Drawings

Planar Upward Drawings C.S. 252 Pro. Rorto Tmssi Computtionl Gomtry Sm. II, 1992 1993 Dt: My 3, 1993 Sri: Shmsi Moussvi Plnr Upwr Drwings 1 Thorm: G is yli i n only i it hs upwr rwing. Proo: 1. An upwr rwing is yli. Follow th