Question

In triangle ABC; D and E are 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

Given: D and F are mid points of AB and AC respectively.
Hence, by mid point theorem, $DF\parallel BC$
Also, given $BD\parallel EF$
Since, opposite sides are parallel to each other. Hence, $BDEF$ is a parallelogram
Perimeter of BDEF = $2(BD+BE)$ (opposite sides of parallelogram are equal)
Perimeter of BDEF = $AB+BC$ (D and E are mid points of AB and BC respectively)
Perimeter of BDEF = $16+18$
Perimeter of BDEF = $34$ cm