Question

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


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Answer 1

Question :-

1. The diagonals of a parallelogram are equal, then show that it is a rectangle.

Solution :-

Let ABCD is a parallelogram such that

AC = BD.

In ∆ABC and ∆DCB,

• AC = DB [Given]
• AB = DC

[Opposite sides of a parallelogram]

• BC = CB [Common]

∴ ∆ABC ≅ ∆DCB [By SSS congruency]

∠ABC = ∠DCB [By C.P.C.T.] …(i)

_____________

Now, AB || DC and BC is a transversal.

[ ∵ ABCD is a parallelogram]

∴ ∠ABC + ∠DCB = 180° …(ii)

[Co-interior angles]

_____________

From (1) and (2), we have

∠ABC = ∠DCB = 90°

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

∴ ABCD is a rectangle

Answer 2

Answer:

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