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101 LearnersLast updated on September 2, 2025
Properties of Diagonals of Rectangle
A rectangle is a type of quadrilateral that has distinct properties, especially concerning its diagonals. These properties assist students in simplifying geometric problems related to rectangles. The properties of a rectangle include having opposite sides that are equal in length and diagonals that bisect each other and are equal in length. These properties help students analyze and solve problems related to symmetry, angles, and area. Now, let us learn more about the properties of the diagonals of a rectangle.
What are the Properties of Diagonals of a Rectangle?
The properties of the diagonals of a rectangle are straightforward, and they help students understand and work with this type of quadrilateral. These properties are derived from the principles of geometry. There are several properties of the diagonals of a rectangle, and some of them are mentioned below:
Property 1: Equality of Diagonals The diagonals of a rectangle are equal in length.
Property 2: Bisection The diagonals of a rectangle bisect each other, dividing each diagonal into two equal parts.
Property 3: Angles The angles formed where the diagonals intersect are not necessarily right angles, unlike in a square.
Property 4: Symmetry The diagonals of a rectangle act as lines of symmetry for the shape.
Property 5: Area Formula The formula used to calculate the area of a rectangle (though not directly related to diagonals) is given by: Area = length x width
Tips and Tricks for Properties of Diagonals of a Rectangle
Students might confuse the properties of diagonals of a rectangle with those of other quadrilaterals. To avoid such confusion, we can follow the following tips and tricks:
- Equality of Diagonals: Students should remember that in a rectangle, both diagonals are always equal in length.
- Diagonals Bisect Each Other: Students should remember that in a rectangle, the diagonals bisect each other, meaning they divide each other into two equal parts when they intersect.
- Non-Perpendicular Diagonals: Students should note that unlike a square, the diagonals of a rectangle do not intersect at right angles.
Confusing a Rectangle with a Square
Students should remember that while both shapes have equal diagonals, only in a square do the diagonals intersect at right angles. In a rectangle, they do not.
Mistake 1
Misinterpreting Diagonal Bisection
Students should know that the diagonals of a rectangle bisect each other, meaning each diagonal divides the other into two equal halves.
Mistake 2
Incorrectly Applying the Area Formula
Students should practice the correct formula used to find the area of a rectangle, which is given by: Area = length x width
Mistake 3
Misunderstanding Angle Relationships
Students should remember that the intersection of diagonals in a rectangle does not form right angles, unlike in a square.
Mistake 4
Forgetting the Equality of Diagonals
Students must remember that in a rectangle, the diagonals are always equal in length.
Mistake 5
Solved Examples on the Properties of Diagonals of Rectangles
In a rectangle, the four corners are marked as A, B, C, and D. If AB = 6 cm, BC = 8 cm, what is the length of diagonal AC?
Diagonal AC = 10 cm.
Problem 1
In a rectangle, the diagonals are equal and can be calculated using the Pythagorean theorem. Diagonal AC = √(AB² + BC²) = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.
In a rectangle ABCD, if the diagonal AC is 13 cm, what is the length of diagonal BD?
Explanation
Diagonal BD = 13 cm.
Problem 2
In a rectangle, the diagonals are equal. Hence, diagonal BD = AC = 13 cm.
The diagonals of a rectangle intersect at point O. If one segment of a diagonal is 5 cm, what is the total length of the diagonal?
Explanation
Total length of the diagonal = 10 cm.
Problem 3
Since diagonals of a rectangle bisect each other and are equal, each segment is half of the diagonal. Thus, total length = 2 x 5 cm = 10 cm.
In rectangle ABCD, if diagonal AC bisects diagonal BD at point E, and BE = 4 cm, what is the length of ED?
Explanation
ED = 4 cm.
Problem 4
Since BE = 4 cm and diagonal BD is bisected by AC, then ED = BE = 4 cm.
A rectangle has diagonals of length 12 cm. If one side of the rectangle is 5 cm, what is the length of the other side?
Explanation
The length of the other side = 7 cm.
A rectangle is a quadrilateral with opposite sides that are equal and all angles equal to 90 degrees.
1.How many equal diagonals does a rectangle have?
2.Do the diagonals of a rectangle bisect each other?
3.Do the diagonals of a rectangle intersect at right angles?
4.How do you find the length of a diagonal in a rectangle?
Common Mistakes and How to Avoid Them in Properties of Diagonals of a Rectangle
Students often get confused when understanding the properties of diagonals of a rectangle, leading to mistakes while solving related problems. Here are some common mistakes students make and solutions to these common mistakes.
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
