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Question: Which of the following statements is/are correct?
1. Diagonals in a rhombus intersect at right angles and in a square the diagonals bisect each other.
2. In a square, the measures of the diagonals are equal, whereas in a rhombus, the measures of the diagonals need not be equal.
3. In a square, each angle is a right angle, whereas in a rhombus each angle need not be a right angle.
4. In a rhombus and a square, the sum of the adjacent angles is 180o.


A ) (1) only
B ) (2) and (3)
C ) (3) and (4)
D ) All the four statements

Steps to derive

1 Rhombus is a parallelogram with four congruent sides. In a rhombus, the diagonals bisect each other at right angles. Since a rhombus is a parallelogram, the sum of the adjacent angles is 180o.

2 A square is a parallelogram with congruent sides and four right angles. In a square, the diagonals bisect each other at right angles. Since a square is a parallelogram, the sum of the adjacent angles is 180o.

3 So, all the four statements are correct.



Hence the right answer is Option D

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