`squareABCD` is a parallelogram. Point `E` is on side `BC`. Line `DE` intersects ray `AB` in point `T`. Prove that `DExxBE=CExxTE`.

square ABCD is a parallelogram point E is on side BC. Line DE intersects ray AB in point T . Prove that DExxBE=CExxTE .

ABCD is a parallelogram and E is a point, on BC. If the diagonal BD intersects AE at F, prove that AFxxFBxxEFxxFD .

squareABCD is a parallelogram. P is any point on side BC. Find two pairs of triangles with equal areas.

In the given figure, ABCD is a parallelogram and E is the midpoint of side BC. If DE and AB when produced meet at F, prove that AF = 2AB.

In the adjoining figure squareABCD is a parallelogeam. Points X and Y lie on the sides AD and BC respectively and AX=1/4ADandCY=1/4BC. Show that squareXBYD is a parallelogram.

The diagonal BD of a parallelogram ABCD intersects the segment AE at the point F, where E is any point on the Side BC. Prove that DFxxEF= FBxxFA .

The diagonal BD of a parallelogram ABCD intersects the segment AE at the point F where E is any point on the side BC. Prove that DFxEF=FBxFA

P is the mid-point of the side CD of a parallelogram ABCD. A line through C parallel to PA intersects AB at Q and DA produced at R. Prove that DA = AR and CQ = QR.

In rectangle ABCD, E is the midpoint of side BC. Prove that, AE = DE.