Concept Overview
A quadrilateral is a closed shape with four sides.
Different quadrilaterals have different side, angle, and diagonal properties.
Properties of Quadrilaterals explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
Step 1
Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
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A quadrilateral is a closed shape with four sides.
Different quadrilaterals have different side, angle, and diagonal properties.
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Every quadrilateral has four sides and four angles.
The sum of interior angles of any quadrilateral is 360 degrees.
A parallelogram has both pairs of opposite sides parallel. Many other quadrilaterals, such as rectangles, squares, and rhombuses, are special types of parallelograms.
Diagonals are line segments joining opposite vertices. Diagonal properties are very useful in exam problems.
Meaning: A quadrilateral is a fouided closed figure.
Definition: A quadrilateral is a polygon with four sides.
A square, rectangle, rhombus, and trapezium are all quadrilaterals.
Meaning: A parallelogram has opposite sides parallel.
Definition: A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
Opposite sides are equal. Opposite angles are equal. Diagonals bisect each other.
Meaning: A rectangle has four right angles. A square has four equal sides and four right angles.
Definition: A rectangle is a parallelogram with four right angles. A square is a rectangle with all sides equal.
A square has the properties of a rectangle and a rhombus.
Meaning: A rhombus has four equal sides.
Definition: A rhombus is a parallelogram with all sides equal.
Easy
Question: Three angles of a quadrilateral are 80 degrees, 90 degrees, and 110 degrees. Find the fourth angle.
Medium
Question: In a parallelogram, one angle is 70 degrees. Find its adjacent angle.
Exam-level
Question: A rhombus has diagonals meeting at O. If one diagonal is 12 cm, find the length from a vertex to O along that diagonal.
Using triangle angle sum for a quadrilateral
Why it happens: 180 degrees is remembered from triangles.
Correct approach: A quadrilateral has angle sum 360 degrees.
Thinking every quadrilateral is a parallelogram
Why it happens: Only special examples are remembered.
Correct approach: Check whether both pairs of opposite sides are parallel.
Mixing rectangle and rhombus diagonal properties
Why it happens: Both are parallelograms.
Correct approach: Rectangle diagonals are equal. Rhombus diagonals are perpendicular.
Is a square a rectangle?
Yes. A square is a special rectangle with all sides equal.
Is every rectangle a square?
No. A rectangle becomes a square only when all four sides are equal.
What does bisect mean?
Bisect means divide into two equal parts.
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Its diagonals bisect each other at right angles.
Meaning: A trapezium has one pair of parallel sides. A kite has two pairs of adjacent equal sides.
Definition: A trapezium is a quadrilateral with one pair of opposite sides parallel.
A kite has equal neighbouring sides, and one diagonal often acts as a line of symmetry.