if the diagonals of a parallelogram are equal then show that it is a rectangle .
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- Parallelogram ABCD , AC = BD
- ABCD is a rectangle.
In ABC and DCB
AB = CD
AC = BD
BC = BC
ABC = DCB
By SSS congruence criteria
∠1 = ∠2
AB || CD
And
∠1 = ∠2 = 180°
2∠1 = 180° --------
∠1 = 90°
∠1 = ∠2 = 90° -------
Also, opposite angles of parallelogram are equal.
∠2 = ∠D = 90°
∠1 = ∠A = 90°
All the angles of parallelogram ABCD are 90°
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