It is easy to prove that a rhombus is a parallelogram whose diagonals meet at right angles. Let the two diagonals of a parallelogram intersect at a point O. If the angle at the point they meet is 90 degrees, then by using Pythagorean theorem each side of the rectangle.
A parallelogram with all four equal sides and right angles is known as the rhombus. Here we will prove that “A Rhombus is a Parallelogram whose diagonals meet at right angles”. If the given figure has right angles then we can say that the given parallelogram is a Rhombus.
A Rhombus is a Parallelogram whose Diagonals Meet at Right Angles
Prove that A Rhombus is a Parallelogram whose Diagonals Meet at Right Angles
Consider the parallelogram ABCD with diagonals AD and BC as shown in the above figure.
And the diagonals meet at the point “O”.
A parallelogram is a rhombus if its adjacent sides are equal.
Consider ΔAOB and ΔAOC
∠AOB = ∠AOC [both 90° because given that diagonals intersect at right angles]
OC = OB [diagonals of a parallelogram bisect each other]
AO is the common side
ΔAOB ≅ ΔAOC
AB = AC [corresponding sides of congruent triangles]
Thus the adjacent sides are equal.
Therefore, we can say that the parallelogram ABCD is a rhombus.
Thus a parallelogram whose diagonals intersect at right angles is a rhombus.
FAQs on a Rhombus is a Parallelogram Diagonals Intersect at Right Angles
1. Do the diagonals of a rhombus meet at right angles?
The diagonals of a rhombus bisect each other at right angles.
2. Do the diagonals of a parallelogram meet at a right angle?
No, as per the rule the diagonals of a parallelogram do not bisect each other at right angles. We know that a parallelogram is a quadrilateral with opposite sides parallel and equal in length. All parallelograms are not squares, the diagonals do not intersect at right angles.
3. Does a rhombus have right angles yes or no?
A square has parallel sides, four right angles, and four equal sides. A square can be a rectangle and a parallelogram. No, because a rhombus does not have to have four right angles.