Question

If AP and DQ are medians of triangles ABC and DEF respectively, where ∆ABC ~ ∆DEF, then prove that `(AB)/(DE) = (AP)/(DQ)`.

Answer 1

Given ΔABC ∼ ΔDEF

`(AB)/(DE) = (BC)/(EF)`

Since AP and DQ are medians.

BP = `(BC)/2`, EQ = `(EF)/2`

So, `(AB)/(DE) = (BC)/(EF) = (2BP)/(2EQ)`

`(AB)/(DE) = (BP)/(EQ)`

In ∆ABP and ∆DEQ

∠B = ∠E   ....(corresponding angles of similar triangles)

∠A = ∠D   ....(corresponding angles of similar triangles)

Thus, ∆ABP ∼ ∆DEQ

Corresponding sides of similar triangles are proportional:

`(AB)/(DE) = (AP)/(DQ)`

Hence proved.