Class 7 Exam > Class 7 Videos > Advance Learner Course: Mathematics (Maths) Class 7 > Proof: Diagonals of a Rectangle are of equal Length and Bisect each other
Proof: Diagonals of a Rectangle are of equal Length and Bisect each other Video Lecture | Advance Learner Course: Mathematics (Maths) Class 7
FAQs on Proof: Diagonals of a Rectangle are of equal Length and Bisect each other Video Lecture - Advance Learner Course: Mathematics (Maths) Class 7
| 1. How can I prove that the diagonals of a rectangle are of equal length? |  |
Ans. To prove that the diagonals of a rectangle are of equal length, you can use the properties of rectangles. Start by drawing a rectangle and labeling its vertices. Then, use the distance formula to find the lengths of the diagonals. By calculating the distances between the vertices, you will find that the lengths of the diagonals are equal.
| 2. Why do the diagonals of a rectangle bisect each other? | |
Ans. The diagonals of a rectangle bisect each other because a rectangle is a parallelogram. In a parallelogram, the diagonals bisect each other, meaning that they divide each other into two equal parts. Since a rectangle is a special type of parallelogram with 90-degree angles, its diagonals bisect each other at their midpoint.
| 3. Can the diagonals of a rectangle have different lengths? | |
Ans. No, the diagonals of a rectangle cannot have different lengths. By definition, a rectangle has four right angles, which makes it a special type of parallelogram. In a parallelogram, the diagonals are always equal in length. Therefore, in a rectangle, the diagonals will always have the same length.
| 4. How can I use the properties of a rectangle to prove that the diagonals bisect each other? | |
Ans. To prove that the diagonals of a rectangle bisect each other, you can use the properties of a rectangle. Since a rectangle is a parallelogram, its diagonals bisect each other. You can show this by drawing a rectangle, labeling its vertices, and drawing the diagonals. Then, using the properties of parallelograms, you can show that the diagonals intersect at their midpoint, dividing each other into two equal parts.
| 5. Can a quadrilateral with equal length diagonals always be considered a rectangle? | |
Ans. No, a quadrilateral with equal length diagonals cannot always be considered a rectangle. While it is true that a rectangle has equal length diagonals, there are other quadrilaterals, such as a rhombus or a square, that also have equal length diagonals. To determine if a quadrilateral is a rectangle, you need to consider additional properties, such as having four right angles.
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