Question

In triangle ABC, D and E are the mid-points of the sides AB and AC, respectively. Through E, a straight line is drawn parallel to AB to meet BC at F. Prove that BDEF is a parallelogram. If AB = 16 cm, AC = 12 cm and BC = 18 cm, find the perimeter of the parallelogram BDEF.

Answer 1

From the figure, since E is the midpoint of AC and EF || AB

Therefore, F is the midpoint of BC, and 2DE = BC or DE = BF

Again, D and E are midpoints; therefore, DE || BF and EF = BD

Hence BDEF is a parallelogram.

Now,

BD = EF = `1/2"AB" = 1/2 xx 16` = 8 cm

BF = DE = `1/2"BC" = 1/2 xx 18` = 9 cm

Therefore perimeter of BDEF = 2(BF + EF) = 2(9 + 8) = 34 cm.