ABC is an isosceles triangle with AB =
AC and BD and CE are its two medians.
Show that BD = CE.
Answers
Answered by
1
Answer:
Given:-
AB = AC
Also , BD and CE are two medians
Hence ,
E is the midpoint of AB and
D is the midpoint of CE
Hence ,
1/2 AB = 1/2AC
BE = CD
In Δ BEC and ΔCDB ,
BE = CD [ Given ]
∠EBC = ∠DCB [ Angles opposite to equal sides AB and AC ]
BC = CB [ Common ]
Hence ,
Δ BEC ≅ ΔCDB [ SAS ]
BD = CE (by CPCT)
Answered by
0
Answer:
A simpler way:
In ∆ABC,
AB = AC (given)
=>
In ∆EBC and ∆DCB,
BC = BC (common side)
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! )
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