Question

In the given figure, D is a point on side BC of a △ ABC and E is a point such that CD = DE. Prove that AB + AC > BE.

Answer 1

Consider △ ABC

We know that

AB + AC > BC

It can be written as

AB + AC > BD + DC

We know that CD = DE

So we get

AB + AC > BD + DE ….. (1)

Consider △ BED

We know that

BD + DE > BE …… (2)

Considering both the equations we get

AB + AC > BE.