ABCD is a square, X is the mid-point of AB and Y the mid-point of BC. Prove that
the triangles ADX and BAY are congruent.

ABCD is a square, X is the mid-point of AB and Y the mid-point of BC. Prove that angle DXA = angle AYB

ABCD is a square, X is the mid-point of AB and Y the mid-point of BC. Prove that DX is perpendicular to AY.

In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.

ABCD is a parallelogram. E is the mid-point of AB and F is the mid-point of CD. GH is any line that intersects AD, EF and BC at G, P and H respectively. Prove that : GP=PH

A B C is a triangle in which D is the mid-point of BC and E is the mid-point of A D . Prove that area of triangle B E D=1/4area \ of triangle A B C . GIVEN : A triangle A B C ,D is the mid-point of B C and E is the mid-point of the median A D . TO PROVE : a r( triangle B E D)=1/4a r(triangle A B C)dot

ABCD is a parallelogram E is mid-point of AB and DE bisects angle D. Prove that BC= BE

ABCD is a parallelogram E is mid-point of AB and DE bisects angle D. Prove that CE bisects angle C

In an equilateral triangle ABC , D is the mid-point of AB and E is the mid-point of AC. Find the ratio between ar ( triangleABC ) : ar(triangleADE)

E is the mid-point of side AB and F is the mid point of side DC of parallelogram ABCD . Prove that AEFD is a parallelogram.

D is the mid-point of side AB of the triangle ABC.E is the mid-point of CD and F is the mid-point of AE. Prove that 8 xx " area of " (DeltaAFD) = " area of " Delta ABC