Question

D and E are respectively the midpoints on the sides AB and AC of a triangle ABC and BC = 6 CM. if DE parallel to BC. THEN WHAT IS THE LENGTH OF DE IN CMS?

Answer 1

Answer:

3Cm

Step-by-step explanation:

DE can't be perpendicular it can be parallel to BC.

In triangleADE and triangle ABC.

DE ll BC

Angle ADE =Angle ABC...(corresponding angles.)

Angle AED =Angle ACB...(corresponding angles.)

By AA test of similarity both triangles are similar.

But,AD=1/2 × AB...(D is the midpoint)

DE=1/2 BC...(c.s.s.t.)

=1/2×6

=3cm.

Answer 2

Mid-Point Theorem

Given:

ABC is a triangle with BC= 6cm and D and E are the midpoints of AB and AC.

DE is parallel to BC.

To find:

Length of DE

Explanation:

An image is attached showing triangle.

Mid-Point Theorem:

It states that the line segment in a triangle joining the midpoint of 2 sides of a triangle is parallel to the third side and the length of line joining midpoints is half of the length of $3_{rd}$ side.

So, BC is the third side and the length of BC is 6cm.

So, $DE=\frac{6}{2} =3cm$

Hence, length of DE is 3cm.