Question

If diagonals of a quadrilateral are equal then show that the figure is a rectangle​

Answer 1

Answer:

Sol: A parallelogram ABCD such that AC = BD In ΔABC and ΔDCB,

AC = DB

[Given]

AB = DC

[Opposite sides of a parallelogram]

BC = CB

[Common]

ΔABC = ΔDCB

[SSS criteria]

∴Their corresponding parts are equal.

⇒∠ABC = ∠DCB

...(1)

∵AB || DC and BC is a transversal.

[∵ ABCD is a parallelogram]

∴∠ABC + ∠DCB = 180°

...(2)

From (1) and (2), we have

∠ABC = ∠DCB = 90°

i.e. ABCD is parallelogram having an angle equal to 90°.

∴ABCD is a rectangle.

Answer 2

Answer : If the diagonals of a parallelogram are equal, then show that it is a rectangle. ... ∴ABCD is a rectangle. Q3. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

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