Question

if the diagonal paramedical then show that it is a rectangle

Answer 1

Heya...

HERE IS YOUR ANSWER...

Q2. If the diagonals of a parallelogram are equal, then show that it is a rectangle.

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.