Question

In an Isosceles triangle ABC(AB=AC).In the triangle ABC,if AB and AC are produced to D and E respectively such that BD=CE,How can Iprove that BE=CD

Answer 1

Here's ur answer :-

In ∆ABC,

AB = AC (given)

=> <ABC = <ACD (opposite sides are equal)

In ∆EBC and ∆DCB,

BC = BC (common side)

<EBC = <DCB ( <ABC = <ACB)

BE = DC (E & D are mid points on AB & AC)

=> ∆EBC is congruent to ∆DCB (by SAS

criteria)

=> BD = CE ( by c.p.c.t ) ( proved)

< refers to angle

Hope this helps you:)