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G.SRL3 Worksheet 7 Guide What is the scale factor from AB to CD? 3',8 -? l,{ *+ k=9 What is the scale factor from CD to AB? What is the EXACT scale factor from (no numericalvalues used here) 641t);1-S l$ to Ig *+ l: n -> *=B What is the general pattern for describing a scale factor? Wr: Qrl-\wagz l") e-"J otf AA Criteria for Similaritv Given: Z-A = Prove: lD MBC - D;\,"t- ZB ZE = LDEF and AW by ffi to b*'B'c' f{ T^*J._1**-*;- ,- yre-\r'^s- ,l\(fr)__ r ii i -ffi, ; -^5. ^- A N ts' Ct b 6 s'rvila^'$ Tr'^s $-,uo(,w (;;to*^-) /, /+ 9 z/*' LB U Lt3' I Aftbc A,B,= )e (W) =-06 Lfr\ U ZD lro,''eihw-- P^n-{+ /-Bt E tv dr' : Dv bfr'E' c' z -f),,r*-12, <- Tv'on-9'-#Ir'<- Pn'uP4 A aer by A AT L 'w ASA (n4/f by a- w\qp/r"E- ilF g'vr'r\\"'- Tto)$'"""b4 l G.SRT.3 Worksheet 7 Guide to map L,BCD onto A,MNp. DB,(MCD) first and translate by vector Cff,, then reflect. ) By construction, use similarity transformations (Hint: (There are many ways to do this construction) NAME: G.SRT.3 WORKSHEET #1 1. Prove that if two triangles have two congruent corresponding angles,,then they must be similar. Given: lA=./.P and lC=lN Prove: AABC'- APMN Bf \, 2. Prove that if two corresponding proportional sides and the included correspo nding congruelt angle (SAS)is enough .l for establishing similarity. Given: lA'=lP and PM ;=; PN B Prove: MBC - APMN ,,:( 3. prove that if two triangles to be similar we need to find a seguence of similarity transformations that rnap AABC on to ADEF. Given: PM BC AB=PN AC-MN Prove: AABC - aPMN G.SRT.3 WORKSHEET #7 4. By construction, use similarity constructions to map AABC onto ANMP. (Hint: Dr., (fdAC) first and then reflect.) (There are many ways to do this construction) 5. By construction, use similarity construction to map MBC onto ANPM. (Hint: D- , (Unc):first and then,ro.tate.) (There are qlqny ways to do this construction) ,,i 2 WORKSHEET#7 #7 G.SRI.3 NAME: NAME: }fu, K, 1.Provethatiftwotriangleshavetwocongruentcorrespondin,.n Given: lA= ZP and ZC= ZN Prove: AABC - ' APMN ^r.r A*ac bb k= %. Lk{tA', Lc?tcl t*'('|= k((4) = Pil /*'TL4z Ly /.ct 2/c; Ll A dV'cte Lfuil bS ArA lrta,l-- A*nL tu A PnN b!- u r^c<-up,ns-o1 tn r"r< g,^^,tS *mtla*ify ta ' --r"A \ \, 2' Prove that if two corresponding proportiohal sides and the included corresponding congruent angle (SAS) is enough for establishing similarity. Given: lA=/.p and PM -PN AB AC B Prove: AABC - APMN 3' Prove that if two triangles to be similar we need to find a sequence of similarity transformations that map AABC on to ADEF. PN MN Glven:PM -----r=AB AC ,BC Prove: MBC - APMN D;lo{- t7*v e b+ k= H A'8, = A (#) = r^, so *L-t k, (?) = & @) =PN,5o .Atct= ?^) r" 6tct* nN f>,ct = B( (m\--Bc(#)= r.,t,N, fr'c' = Aftac'y Apuru bg ss Apnc n- b PUtl 6g a- ruapo'1 ' nf' vn''W 1,o',n'$r't'"*!)'t*9 G.SRT.3 WORKSHEET #7 2 4. By construction, use similarity constructions to map AABC onto ANMp. (Hint: Dr,, (LAAC) first and then reflect.) (There are many ways to do this construction) l' ; A E. 5. By construction, use similarity construction to map AABC onto ANpM. (Hint: D, , (UnC) first and then rotate.) (There are many ways t_o do this construction) o', lnr Da,{- 6,+0.) \rI T a73, (aAut) ,L R ,,,o0, (L frt'g' ,c*)