Question

In the given figure, AC and BD are the diagonals of kite ABCD with AB = AD while AG and ME are the diagonals of rectangle AEGM . If AD = DG and BG is a line segment, then x โ y equals

Answer 1

ABCD is a kite and AB=AD and BC=CD.

EFGH are mid points of AB ,BC,CD,AD

To prove that  EFGH is a rectangle.

For Construction we will join AC and BD.

In ΔABD , E and F are mid points.

so we can write ,EF ║BD and

EF = 1/2 BD   (this is an equation 1)

Now , in Δ BCD , G and H are mid points.

So, GH║ BD and

GH=1/2 BD  (this is an equation 2)

From (1) and (2) EF║ GH and EF = GH ( opposite sides of quad.

EFGH are parallel and equal so EFGH is a parallelogram)

Now since ABCD is a kite ,diagonal intersect at 90

So ∠AOd= 90