Question

Abc is an iscosceles triangle with ab=ac and bd and ce are its two medians show that bd = ce

Answer 1

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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