In ` /_\A B C ,D` is the mid-point of `BC and ED` is the bisector of the `/_ADB and EF` is drawn parallel to `B C` cutting `A C` in `F` . Prove that `/_E D F` is a right angle.

In A B C ,\ D and E are the mid-points of A B and A C respectively. Find the ratio of the areas of A D E and A B C .

A D is a median of Delta A B C . The bisector of /_A D B and /_A D C meet AB and AC in E and F respectively. Prove that EF||BC

In Figure, A B C D isa trapezium in which side A B is a parallel to side D C and E is the mid-point of side A D . If F is a point on the side B C such that the segment E F is parallel to side D C . Prove that F is the mid point of B C and E F=1/2(A B+D C) .

In Figure, A B C D isa trapezium in which side A B is a parallel to side D C and E is the mid-point of side A Ddot If F is a point on the side B C such that the segment E F is parallel to side D C . Prove that F is the mid point of B C and E F=1/2(A B+D C)dot

Let A B C be a triangle with A B=A Cdot If D is the midpoint of B C ,E is the foot of the perpendicular drawn from D to A C ,a n dF is the midpoint of D E , then prove that A F is perpendicular to B Edot

ABCD is a trapezium in which A B\ ||\ D C , BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F (see Fig. 8.30). Show that F is the mid-point of BC.

A B C D is a rhombus, E A B F is a straight line such that E A=A B=B F . Prove that E D and F C when produced meet at right angles.

A B C D is a rhombus, E A B F is a straight line such that E A=A B=B F . Prove that E D and F C when produced meet at right angles.

In Figure, D ,E and F are, respectively the mid-points of sides B C ,C A and A B of an equilateral triangle A B C . Prove that D E F is also an equilateral triangle.

In Figure, D ,E and F are, respectively the mid-points of sides B C ,C A and A B of an equilateral triangle A B C . Prove that D E F is also an equilateral triangle.