Q2 of 24 Page 157

D and E lie on AB and AC respectively of the triangle ABC such that, AB and Let us prove that, DE || BC and


In ΔABC, Let F and G be the midpoint of AB and AC respectively.


So, in ΔAFG, and ,


⇒ D and E are the midpoint of AF and AG respectively.


By applying the theorem:-


The line segment joining the midpoints of two side of a triangle is parallel to the third side and equal to half of it, we get,


and DE || FG ……… (1)


Also, by using above theorem in ΔABC, we get,


and FG || BC ……… (2)


From equations (1) and (2), we get


and DE || BC


More from this chapter

All 24 →
1

In the triangle ABC, D is the midpoint of the side BC; From the point D, the parallel straight lines of CA and BA intersect the sides BA and CA at the points E and F respectively. Let us prove that,

3

In the triangle PQR, the midpoints of the sides QR and QP are X and Z respectively. The side QP is extended upto the points S so that PS = ZP. SX intersects the side PR at the point Y. Let us prove that,

4

Let us prove that, the quadrilateral formed by joining midpoints of consecutive sides of a parallelogram is a parallelogram.

 5

Let us prove that, the quadrilateral formed by joining midpoints of consecutive sides of a rectangular figure is not a square figure but a rhombus.