all ngieS O1Fig. 3.IL7. In figure 5.13 âĄABCD is a parallelo-gram.

1.	all ngieS O1Fig. 3.IL7. In figure 5.13 âĄABCD is a parallelo-gram. Point E is on the ray AB suchthat BE AB then prove that line EDbisects seg BC at point FFig. 5.13
Answer» ABCD is a parallelogram . Point E is on the ray AB such that BE = AB . To prove : BF = FC Proof : i ) AB = DC [ opposite sides ] AB = BE ( given ) DC = BE --- ( 1 ) ii ) In ∆DCF and ∆EBF <FDC = <FEB [ alternate angles ] DC = BE ( S ) [ from ( 1 ) ] <DFC = <EFB [ veritically opposite angles ] Therefore , ∆DCF is congruent to ∆EBF [ ASA congruence Rule ] CF = FB [ CPCT ]

all ngieS O1Fig. 3.IL7. In figure 5.13 âĄABCD is a parallelo-gram. Point E is on the ray AB suchthat BE AB then prove that line EDbisects seg BC at point FFig. 5.13

Answer»

ABCD is a parallelogram .

Point E is on the ray AB such that

BE = AB .

To prove : BF = FC

Proof :

i ) AB = DC [ opposite sides ]

AB = BE ( given )

DC = BE --- ( 1 )

ii ) In ∆DCF and ∆EBF

<FDC = <FEB [ alternate angles ]

DC = BE ( S ) [ from ( 1 ) ]

<DFC = <EFB [ veritically opposite angles ]

Therefore ,

∆DCF is congruent to ∆EBF

[ ASA congruence Rule ]

CF = FB [ CPCT ]