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. ​

Answer 1

Answer:

Given: D and F are mid points of AB and AC respectively.

Hence, by mid point theorem, DF∥BC

Also, given BD∥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