Question

ABC is an isosceles triangle with AB=AC and BD and CE are it's two medians. Show that BD=CE

Answer 1

Answer:

Step-by-step explanation:

in ABD and ACE

AB = AC

1/2 AB = 1/2 AC

AE = AD

∠A = ∠A (common angle)

AB = AC  (given)

ABD ≅ ACE (SAS)

BE = CE

hence proved

please mark as the brainliest answer....

Answer 2

Answer:

A simpler way:

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! )