Mathematics Concept Notes for Class 8: Ganita Prakash Part 1 Chapter 04 Quadrilaterals
Explore reliable concept summaries and revision materials through the CBSE Class 8 Mathematics Quadrilaterals Notes Set 02. Tailored for Class 8 learners, utilizing these notes for Mathematics Ganita Prakash Part 1 Chapter 04 Quadrilaterals ensures thorough preparation and strengthens core academic definitions before final evaluations.
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Access the complete concept summary PDF for Ganita Prakash Part 1 Chapter 04 Quadrilaterals below. Regular review of these targeted notes builds familiarity with complex Class 8 Mathematics themes and helps secure higher marks in final school evaluations.
Angle Sum and Exterior Angles
A quadrilateral has four sides, four vertices, four angles and two diagonals. A diagonal splits it into two triangles, so the four interior angles add up to 2 × 180° = 360°. Taking one exterior angle at each vertex (sides produced in order), the four exterior angles also add up to 360°.
For a regular polygon of n sides each exterior angle is 360°/n and each interior angle is 180° − 360°/n.
Family of Quadrilaterals
Trapezium: exactly one pair of parallel sides. Kite: two pairs of equal adjacent sides. Parallelogram: both pairs of opposite sides parallel. Rectangle: a parallelogram with a right angle. Rhombus: a parallelogram with all sides equal. Square: a rectangle with all sides equal, which is also a rhombus.
Every square, rectangle and rhombus is a parallelogram. A kite and a general trapezium are not parallelograms.
Properties of a Parallelogram
Opposite sides are equal and opposite angles are equal. Adjacent angles add up to 180°. The diagonals bisect each other, and each diagonal splits the parallelogram into two congruent triangles.
Converses: a quadrilateral is a parallelogram if both pairs of opposite sides are equal, or both pairs of opposite angles are equal, or the diagonals bisect each other, or one pair of opposite sides is both equal and parallel.
Diagonals at a Glance
Parallelogram: bisect each other. Rectangle: equal and bisect each other. Rhombus: perpendicular, bisect each other and bisect the angles. Square: equal, perpendicular and bisect each other. Kite: perpendicular. Isosceles trapezium: equal.
A parallelogram with equal diagonals is a rectangle; a parallelogram with perpendicular diagonals is a rhombus; both together give a square.
Mid-point Theorem
The segment joining the mid-points of two sides of a triangle is parallel to the third side and half as long. Conversely, a line through the mid-point of one side parallel to a second side bisects the third side. Joining the mid-points of the sides of any quadrilateral in order gives a parallelogram.
Worked Examples
Example 1: The angles of a quadrilateral are in the ratio 2 : 3 : 4 : 6. Then 15x = 360°, so x = 24° and the angles are 48°, 72°, 96° and 144°.
Example 2: In a rhombus the diagonals are 24 cm and 10 cm. Half-diagonals are 12 and 5, so each side is √(144 + 25) = 13 cm and the perimeter is 52 cm.
Example 3: One angle of a parallelogram is 3 times its adjacent angle. Then 4x = 180°, so the angles are 45° and 135°.
Example 4: In triangle ABC, D and E are mid-points of AB and AC. If DE = 6.5 cm then BC = 13 cm.
Free study material for Mathematics
Ganita Prakash Part 1 Chapter 04 Quadrilaterals Concepts and Summary for Class 8 Mathematics
About Ganita Prakash Part 1 Chapter 04 Quadrilaterals Revision Notes
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Yes, our CBSE Class 8 Mathematics Quadrilaterals Notes Set 02 include 50% competency-based questions with focus on core logic, keyword definitions, and the practical application of Mathematics principles which is important for getting more marks in 2026 CBSE exams.
Yes, our CBSE Class 8 Mathematics Quadrilaterals Notes Set 02 provide a detailed, topic wise breakdown of the chapter. Fundamental definitions, complex numerical formulas and all topics of CBSE syllabus in Class 8 is covered.
These notes for Mathematics are organized into bullet points and easy-to-read charts. By using CBSE Class 8 Mathematics Quadrilaterals Notes Set 02, Class 8 students fast revise formulas, key definitions before the exams.
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