Question

D,E and F are the midpoints of the sides of triangle ABC. Prove that perimeter of triangle DEF is half of the perimeter of triangle ABC

Answer 1

Step-by-step explanation:

let sides AB=2a, BC=2b, AC=2c

given D, E, F are midpoints

by midpoint thm DE=1/2*BC =1/2*2b=b

similarly EF=1/2*AB=1/2*2a=a

DF=1/2*AC=1/2*2c=c

from above analysis we see that preimetre of triangle ABC=2(a+b+c) and perimetre of triangle DEF=a+b+c

by this we prove that triangle DEF perimetre is 1/2 of perimetre of triangle ABC

Answer 2

perimeter of triangle ABC= 2(a+b+c)

perimeter of triangle DEF= a+b+c.

hence triangle DEF = 1/2 perimeter of triangle ABC