Question

If the diagonals of a parallelogram are equal then show that it is a square​

Answer 1

Answer:

Answer. Given that the diagonals AC and BD of parallelogram

Step-by-step explanation:

ABCD are equal in length . ... Therefore, parallelogram ABCD is a rectangle since a parallelogram with one right interior angle is a rectangle.

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Answer 2

Given that :

AC = BD

Consider the triangle, ∆DAB & ∆CBA

AC = BD (given)

AB = AB (common side)

AD = BC (opposite side)

Therefore, ∆DAB ≈ ∆CBA (By SSS congruent rule)

$\angle\sf{DAB}$ = $\angle\sf{CBA}$ (By CPCT)

If ABCD is parallelogram,

$\angle\sf{DAB}$ + $\angle\sf{CBA}$ = 180°

$\angle\sf{DAB}$ + $\angle\sf{DAB}$ = 180°

$\therefore$ 2 $\angle\sf{DAB}$ = 180°

$\angle\sf{DAB=90°}$

Similarly, $\angle\sf{CBA= 90°}$

$\therefore$ ABCD is a square.