Class 9 Exam > Class 9 Videos > Mathematics (Maths) Class 9 > Theorem Diagonals of a Rhombus are Perpendicular to each other (Easy Explanation)
Theorem Diagonals of a Rhombus are Perpendicular to each other (Easy Explanation) Video Lecture | Mathematics (Maths) Class 9
FAQs on Theorem Diagonals of a Rhombus are Perpendicular to each other (Easy Explanation) Video Lecture - Mathematics (Maths) Class 9
| 1. What is a rhombus? |  |
Ans. A rhombus is a quadrilateral with all four sides of equal length. It is also known as a diamond shape.
| 2. How can we prove that the diagonals of a rhombus are perpendicular to each other? | |
Ans. To prove that the diagonals of a rhombus are perpendicular to each other, we can use the property that the opposite sides of a rhombus are parallel. By drawing the diagonals, we can form four congruent right-angled triangles. Using the Pythagorean theorem, we can show that the diagonals are perpendicular.
| 3. What is the Pythagorean theorem? | |
Ans. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. It is represented by the equation a^2 + b^2 = c^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
| 4. Can a rhombus have diagonals of different lengths? | |
Ans. No, in a rhombus, both diagonals are always of equal length. This is because a rhombus has congruent opposite sides, and the diagonals bisect each other at right angles, dividing the rhombus into four congruent right-angled triangles.
| 5. Are all quadrilaterals with perpendicular diagonals rhombuses? | |
Ans. No, not all quadrilaterals with perpendicular diagonals are rhombuses. While a rhombus has perpendicular diagonals, there are other quadrilaterals like squares and kites that also have perpendicular diagonals. A rhombus is a specific type of quadrilateral with equal side lengths, while squares have equal side lengths and right angles, and kites have two pairs of adjacent sides that are equal.
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