For given isosceles triangle abc, with ab = ac and bd and ce are its two medians then bd = ce
For given question,
We have been given triangle abc is an isosceles triangle with bd = ce
bd and ce are its two medians
As bd is median, d is the midpoint of side ac.
Using midpoint property,
⇒ ad = ac
Similarly, as ce is median, e is the midpoint of side ab.
Using midpoint property,
⇒ ae = eb
For Δabd and Δace,
ab = ac .......................(given)
⇒ ae + eb = ad + dc
⇒ 2 ae = 2 ad
⇒ ae = ad
Also, ∠a = ∠a ....................(common angle)
So, using SAS postulate of triangle congruence,
Δabd ≅ Δace
By Corresponding parts of congruent triangles are congruent,
⇒ bd = ce
Hence proved.
For given isosceles triangle abc, with ab = ac and bd and ce are its two medians then bd = ce
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