Question

In the given figure,prove that the diagonals of a rectangle are equal

Answer 1

In ∆ABD and ∆ABC

AD=BC

AB=AB(common)

angle A= angle B (all angles of rectangle is 90°)

therefore ∆ABD =~ ∆ABC

AC= DB by cpct

hence diagonals of rectangle are equal




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Answer 2

ABCD is a rectangle.

AC and BD are the diagonals of rectangle.

In ΔABC and ΔBCD, we have

AB = CD (Opposite sides of rectangle are equal)

∠ABC = ∠BCD ( Each equal to 90°)

BC = BC (Common)

∴ ΔABC ΔBCD (SAS congruence criterion)

⇒ AC = BD [c.p.c.t]

Hence, the diagonals of a rectangle are equal.

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