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In the given figure, AC=AE, AB=AD and an...

In the given figure, `AC=AE, AB=AD` and `angleBAD=angleEAC`. Prove that `BC=DE`.

Text Solution

Verified by Experts

Since `angle1=angle2` (given)
`:. angle1+angle3=angle2+angle3` (adding same angle on both sides)
`implies" "angle BAC=angleDAE`
Now, in `DeltaBAC` and `DeltaDAE`
`:' {(AB=AD,"(given)"),(angleBAC=angleDAE,"(just proved)"),(AC=AE,"(given)"):}`
`:. DeltaBAC cong DeltaDAE` (SAS)
`:. BC=DE` (c.p.c.t) Hence Proved.
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