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5. In quadrilateral ABCD, AD=CD andAB=CD and |
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Answer» Given A quadrilateral ABCD in which AB=AD and the bisectors of ∠BAC and ∠CAD meet the sides BC and CD at E and F respectively. To prove EF||BD Construction Join AC, BD and EF. Proof In △CAB, AE is the bisector of ∠BAC. ∴ AB AC
= BE CE
.......(i) In △ACD, AF is the bisector of ∠CAD. ∴ AD AC
= DF CF
⇒ AB AC
= DF CF
[∵ AD=AB]........(ii) From (i) and (ii), we GET
BE CE
= DF CF
⇒ EB CE
= FD CF
Thus, in △CBD, E and F divide the sides CB and CD respectively in the same ratio. Therefore, by the converse of Thale's Theorem, we have EF∣∣BD Step-by-step EXPLANATION: i hope help you |
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