Question

in triangle ABC, d and e are the midpoint of ab and ac respectively and FE||BA=12cm prove that (1) f is midpoint of bc. 2)if DE=12cm and AD=18cm . find the value of DB and BF​

Answer 1

Step-by-step explanation:

Given: AB = 12cm, AD =8cm, AB = 12cm and AC = 18cm

To Prove: DE∥BC

in ∆ABC,

DBAD=AB−ADAD=12−88=2

And AEAC=AC−ECAE=18−1212=2

Then, DBAD=ECAE 

Basic Proportionality theorem which states that

if a line is drawn parallel to one side of a triangle the other two sides in distinct points, then the other two sides are divided in the same ratio. 

Hence, DE∥BC

[by converse of basic

proportionality theorem] 

Hence, Proved.