## Pove that the sum of any two side of a triangle is greater than twice the median drow to the third side.it

Question

Lost your password? Please enter your email address. You will receive a link and will create a new password via email.

## Answers ( )

Step-by-step explanation:Given : Triangle ABC in which AD is the median.

To prove:AB+AC>2AD Construction :

Extend AD to E such that AD=DE. Now join EC.

Proof:

In AADB and AEDC AD=DE[ By construction]

D is the midpoint BC.[DB=DB]

AADB=AEDC [vertically opposite angles]

Therefore A ADB = AEDC [ By SAS congruence criterion.]

–> AB=ED[Corresponding parts of congruent triangles ]

In ΔΑEC , AC+ED> AE [sum of any two sides of a triangle is greater than the third side] AC+AB>2AD[AE=AD+DE=AD+AD=2AD

and ED=AB]

Hence proved