A transversal intersect two parallel lines. Prove that the bisector of any pair of corresponding angels so formed are parallel .
Answers
Given:
A transversal PQ cuts two lines AB and CD at E and F respectively.EG and FH are the bisectors of a pair of corresponding angles <PEB and
<EFD respectively such that EG||FH
To prove:
AB||CD
proof:-
EG||FH are cut by transversal EF
<PEG=<EFH {corresponding angle}
<GEB=<HFD
2<GEB=2<HFD
<PEB=<EFD {<GEB=1/2<PEB and <HFD=1/2<EFD}
But these corresponding angles when AB and CD are cut by the transversal PQ.
Therefore;
AB||CD {by corres. <s axiom}
Given: AB and CD are two straight lines cut by a transversal EF at G and H respectively. GM and HN are the bisectors of corresponding angles ∠EGB and ∠GHD respectively such that GM || HN
To prove - AB || HN
Proof:-
GM || HN
⇒∠1 = ∠2 (corresponding angle)
⇒2∠1 = 2∠2 ⇒∠EGB =∠GHD ⇒AB || CD
(∠EGB & ∠GHD are corresponding angles formed by transversal EF with AB and CD and are equal.)
Hence, proved.