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Maths-

General

Easy

Question

In the given picture, if AB = FE, BC = ED, $AB perpendicular BD$ and $FE perpendicular EC$ , then prove that AD = FC.

hint Hint:

prove the given condition by using similarity of triangles

The correct answer is: Hence proved

In $straight capital delta$ ABD and $straight capital delta$ FEC
AB = FE (given)
BC = ED (given)
Now adding CD on both side to above condition ,
BC + CD = ED + CD
BD = CE
∠ ABD = ∠ FEC (as AD = AE)
By SAS rule , $straight capital delta$ ABD ≅ $straight capital delta$ FEC
Then , by congruence AD = FC
Hence proved

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