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102 LearnersLast updated on September 3, 2025
Properties of Rectangle Diagonal
A rectangle is a type of quadrilateral that has specific properties, especially regarding its diagonals. Understanding these properties helps students solve geometric problems related to rectangles. The properties of a rectangle include equal diagonals that bisect each other. These properties assist students in analyzing and solving problems related to symmetry, angles, and area. Now let us learn more about the properties of a rectangle's diagonals.
What are the Properties of a Rectangle's Diagonal?
The properties of a rectangle's diagonal are simple and help students understand and work with this type of quadrilateral. These properties arise from fundamental geometric principles. There are several properties of a rectangle's diagonal, including:
Property 1: Equal Diagonals: The diagonals of a rectangle are equal in length.
Property 2: Diagonal Bisecting Each diagonal bisects the other, dividing each into two equal parts.
Property 3: Symmetry: The diagonals of a rectangle intersect at the center, providing symmetry.
Property 4: Right Angle Intersection In a rectangle, diagonals do not intersect at right angles, unlike some other quadrilaterals.
Property 5: Relation to Area: The diagonals are related to the area through the Pythagorean theorem, as the diagonal acts as the hypotenuse of a right triangle formed by the rectangle's sides.
Tips and Tricks for Properties of a Rectangle's Diagonal
Students often confuse and make mistakes while learning about the properties of a rectangle's diagonals. To avoid confusion, consider these tips and tricks:
Equal Diagonals: Students should remember that in a rectangle, the diagonals are always equal in length. To verify this, students can draw a rectangle and measure the diagonals.
Diagonals Bisect Each Other: Students should remember that in a rectangle, each diagonal bisects the other into two equal segments.
Center Intersection: Students should note that the diagonals intersect at the rectangle's center, which can be verified by folding the rectangle along the diagonals.
Confusing a Rectangle with a Square
Students should remember that while both rectangles and squares have equal diagonals, all sides of a square are equal, whereas opposite sides of a rectangle are equal.
Mistake 1
Misinterpreting the Diagonal Intersection
Students should understand that the diagonals of a rectangle bisect each other but do not intersect at right angles.
Mistake 2
Incorrectly Applying the Pythagorean Theorem
Students should practice using the Pythagorean theorem to relate the sides and diagonals of a rectangle: \(d = \sqrt{l^2 + w^2}\), where \(d\) is the diagonal, \(l\) is the length, and \(w\) is the width.
Mistake 3
Misunderstanding Angle Relationships
Students should remember that the angles formed by the intersection of the diagonals are not necessarily equal or right angles in a rectangle.
Mistake 4
Forgetting the Equal Diagonal Rule
Students must remember that in a rectangle, the diagonals are always equal in length.
Mistake 5
Solved Examples on the Properties of Rectangle Diagonals
In a rectangle, the four corners are marked as A, B, C, and D. If AB = 5 cm, BC = 12 cm, what is the length of diagonal AC?
AC = 13 cm.
Problem 1
Using the Pythagorean theorem, AC = √{AB² + BC²} = √{5² + 12²} = √25 + 144 = √169 = 13) cm.
In a rectangle ABCD, the length of diagonal AC is 15 cm. If AB = 9 cm, what is the length of the side BC?
Explanation
BC = 12 cm.
Problem 2
Using the Pythagorean theorem, (AC² = AB² + BC²). Substituting the values, (15² = 9² + BC²). Solving, we get (225 = 81 + BC²), so (BC² = 144), therefore (BC = 12) cm.
The diagonals of a rectangle intersect at point O. If the length of one diagonal is 16 cm, what is the length of half of each diagonal?
Explanation
Each half of the diagonal is 8 cm.
Problem 3
Since the diagonals of a rectangle bisect each other, each half of the diagonal is (16/2 = 8) cm.
In rectangle ABCD, diagonal AC bisects diagonal BD. If BE = 4 cm, what is the length of ED?
Explanation
ED = 4 cm.
Problem 4
Since the diagonals bisect each other, ED = BE = 4 cm.
A rectangle has sides of length 6 cm and 8 cm. What is the length of the diagonal?
Explanation
Diagonal = 10 cm.
A rectangle is a quadrilateral with opposite sides equal and all angles equal to 90 degrees.
1.How many pairs of equal sides does a rectangle have?
2.Are the diagonals of a rectangle equal?
3.How do you find the length of a rectangle's diagonal?
4.Can the diagonals of a rectangle be perpendicular?
Common Mistakes and How to Avoid Them in Properties of Rectangle Diagonals
Students often get confused about the properties of a rectangle's diagonals, leading to errors when solving related problems. Here are common mistakes and solutions to these issues.
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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.
