Question

State true or false:

If $ED=EC$, then $AB+AD>BC$.(Refer given fig.)

• A. True
• B. False

Answer 1

The correct option is A True

In $△ABD$, we have sum of two sides $>$ third side
$=>AB+AD>BD$ OR

$=>AB+AD>BE+ED--\left(1\right)$
Also, in $△BCE$, we have sum of two sides $>$ third side
$=>EB+EC>BC$ ---- (2)
Adding equations $1,2$ we get
$=>AB+AD+EB+EC>BE+ED+BC$
$=>AB+AD+EC>ED+BC$

But $EC=ED$

Hence, $AB+AD>BC$