Schooling · Class 8 · Mathematics · Quadrilaterals · Chapter on a page
CBSE Class 8 · Mathematics · NCERT Ganita Prakash Part-I
Quadrilaterals: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- A quadrilateral has four vertices…
- A trapezium has at least one pair of…
- A parallelogram has both pairs of…
- A rhombus is a parallelogram with…
- A rectangle is a parallelogram with…
- A square is both a rhombus and a…
- A kite has two pairs of adjacent…
- Formulas and facts
- Sum of angles of a quadrilateral =…
- Fact / Formula
- Diagonals of a rhombus bisect at 90°
- Diagonals of a rectangle are equal
- Watch out for
- Adding four angles and expecting 180°
- Thinking all parallelograms have 90°…
- Believing diagonals of every…
- Confusing bisect with perpendicular…
- Labelling a kite as a parallelogram
What this chapter is about
A quadrilateral is a closed figure made of four straight sides. You see quadrilaterals everywhere: the top of your desk, a kite, a cricket pitch, floor tiles, window panes. In earlier classes you learnt about triangles and their angle sum. Now you will extend that idea to four-sided figures and discover that the sum of interior angles of every quadrilateral is 360°.
Key ideas
- A quadrilateral has four vertices, four sides and four interior angles. The sum of its interior angles is always 360°.
- A trapezium has at least one pair of opposite sides parallel.
- A parallelogram has both pairs of opposite sides parallel. Its opposite sides are equal, opposite angles are equal, and the diagonals bisect each other (cut each other into two equal parts).
- A rhombus is a parallelogram with all four sides equal. Its diagonals bisect each other at right angles.
- A rectangle is a parallelogram with all four angles equal to 90°. Its diagonals are equal in length and bisect each other.
- A square is both a rhombus and a rectangle: all sides equal, all angles 90°, diagonals equal and bisecting at right angles.
- A kite has two pairs of adjacent sides equal. Its diagonals are perpendicular, and one diagonal bisects the other.
Formulas and facts to remember
- Fact / Formula: Sum of angles of a quadrilateral = 360° · Meaning: Add all four interior angles; the total is always 360°.
- Fact / Formula: Opposite sides of a parallelogram are equal · Meaning: If ABCD is a parallelogram, AB = CD and AD = BC.
- Fact / Formula: Opposite angles of a parallelogram are equal · Meaning: ∠A = ∠C and ∠B = ∠D.
- Fact / Formula: Consecutive angles of a parallelogram are supplementary · Meaning: ∠A + ∠B = 180°.
- Fact / Formula: Diagonals of a parallelogram bisect each other · Meaning: They meet at a point that is the midpoint of each diagonal.
- Fact / Formula: Diagonals of a rhombus bisect at 90° · Meaning: They cross at right angles.
- Fact / Formula: Diagonals of a rectangle are equal · Meaning: Each diagonal has the same length.
Common mistakes
- Adding four angles and expecting 180° → Remember that 180° is for a triangle; a quadrilateral's angles add to 360°.
- Thinking all parallelograms have 90° angles → Only rectangles and squares have all right angles; a general parallelogram does not.
- Believing diagonals of every parallelogram are equal → Diagonals are equal only in a rectangle (and square), not in a general parallelogram or rhombus.
- Confusing bisect with perpendicular bisect → In a parallelogram diagonals bisect each other but are not necessarily perpendicular; in a rhombus they are both.
- Labelling a kite as a parallelogram → A kite has adjacent sides equal, not opposite sides; it is not a parallelogram unless it is a rhombus.
Quick revision
- Angle sum of any quadrilateral = 360°.
- Parallelogram: opposite sides equal, opposite angles equal, diagonals bisect each other.
- Rhombus: all sides equal, diagonals bisect at 90°.
- Rectangle: all angles 90°, diagonals equal.
- Square: all sides equal, all angles 90°, diagonals equal and perpendicular.
- Trapezium: at least one pair of parallel sides.