The square ABGH and ADEF are drawn on the sides AB and AD of a parallelogram ABCD. Prove (i) `/_FAH = /_ABC,` (ii) FH = AC.

The given figure shows a parallelogram ABCD. Squares ABPQ and ADRS are drawn on sides AB and AD of the parallelogram ABCD. Prove that : (i) angle SAQ = angle ABC (ii) SQ = AC

The given figure showns a parallelogram ABCD. Squares ABPQ and ADRS are drawn on sides AB and AD respectively of the parallelogram ABCD. Prove that : (i) angleSAQ=angleABC (ii) SQ=AC

Two circles are drawn with sides AB and AC of a triangle ABC as diameters

Equilateral triangles ABD and ACE are drawn on sides AB and AC respectively of a DeltaABC outside it. Prove that : (i) angleDAC= angleEAB (ii) DC = BE

Equilateral triangles ABD and ACE are drawn on sides AB and AC respectively of a DeltaABC outside it. Prove that : (i) angleDAC= angleEAB (ii) DC = BE

In the figure given alongside, squares ABDE and AFGC are drawn on the side AB and the hypotenuse AC of the right triangle ABC. If BH perpendicular to FG, prove that : (i) DeltaEAC~=DeltaBAF . (ii) Area of the square ABDE = Area of the rectangle ARHF.

In the figure given alongside, squares ABDE and AFGC are drawn on the side AB and the hypotenuse AC of the right triangle ABC. If BH perpendicular to FG, prove that : (i) DeltaEAC~=DeltaBAF . (ii) Area of the square ABDE = Area of the rectangle ARHF.

In the diagram below, P and Q are midpoints of sides BC and AD respectively of the parallelogram ABCD. If side AB = diagonal BD: prove that the quadrilateral BPDQ is a rectangle.

vec(AC) and vec(BD) are the diagonals of a parallelogram ABCD. Prove that (i) vec(AC) + vec(BD) - 2 vec(BC) (ii) vec(AC) - vec(BD) - 2vec(AB)

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.