Question

triangle ABC,D is the midpoint of BC, MN||BC, and AD intersects MN at point E

PROVE THAT: ME=EN​

Answer 1

heya mate.. here's ur answer..

in tri AME and ABD ,

since MN parallel BC.. SO...

ang AME =ang ABD

and ang AEM =ang ADB

tri AME similar tri ABD (by AA similarity)

so.. ME /BD =AE/AD...(1)

similarly, tri AEN similar tri ADC

SO. ..EN/DC=AE/AD...(2)

NOW... from 1 and 2

ME /BD=EN/DC

HENCE.... ME =EN

(because D is the midpoint of BC so BD =DC)

THANKS.. hope this helps you ...

Answer 2

Given: ABC is a triangle,D is the midpoint of BC ,MN||BC and AD intersects MN at point E

To prove:ME=EN

Prove: In/\ ABC

/_ ABD=/_ ADC

AD=AD(common)

BD=CD (BASE)

M is a midpoint of AB

D is a midpoint of BC

N is a midpoint of AC

E is a midpoint of AD

In /\ ABD:

M is a midpoint of AB

and E is a midpoint of AD

AM=MB (linear pair)

AE=AD

/\ABD is half of angle ABC

ME||BD

SAME in triangle ADC

so the formula of con.....the mid...theorem

ME||NE

PROVED.....