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Grade 8/ Mathematics/ Quadrilaterals
Chapter 4 · NCERT Class 8 Ganita Prakash

Quadrilaterals

Four sides, four corners — and a whole family of shapes that share a secret: their angles always add to 360°. Squares, rectangles, rhombuses and parallelograms are all cousins, and their diagonals give each one away. Tap each idea to see how it works.

📐 3 topics⏱ ~25 min📝 12-question quiz
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The six ideas of quadrilaterals

The parallelogram family is easy to mix up. Tap each shape to see what makes it special and how its diagonals behave.

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The three big ideas

  • A quadrilateral is a closed figure with 4 sides, 4 vertices, 4 angles and 2 diagonals.
  • The angle sum is always 360°. Draw one diagonal and the quadrilateral splits into two triangles; each triangle\u2019s angles add to 180°, so 2 × 180° = 360°.
  • Common types: trapezium (one pair of parallel sides), parallelogram (two pairs), rhombus, rectangle, square and kite.

Worked example. Three angles of a quadrilateral are 95°, 85° and 100°. Find the fourth.

1. All four angles add to 360°.

2. Known angles: 95° + 85° + 100° = 280°.

3. Fourth angle = 360° − 280° = 80°.

  • Parallelogram — opposite sides parallel and equal; opposite angles equal; adjacent angles supplementary (add to 180°); diagonals bisect each other.
  • Rectangle — a parallelogram with all angles 90°. It keeps every parallelogram property and adds equal diagonals.
  • Rhombus — a parallelogram with all sides equal. Its diagonals are perpendicular (cross at 90°).
  • Square — both at once: all sides equal AND all angles 90°. So it is a rhombus and a rectangle together.

Worked example. One angle of a parallelogram is 70°. Find the other three angles.

1. Opposite angle is equal: 70°.

2. Adjacent angles are supplementary: 180° − 70° = 110°.

3. So the angles are 70°, 110°, 70°, 110°. Check: 70 + 110 + 70 + 110 = 360°. ✓

Common mistake: assuming every parallelogram has right angles or equal diagonals. Only a rectangle or square does — a slanted parallelogram has neither.
  • Parallelogram: diagonals bisect each other (cut each other in half) — but they are unequal and not perpendicular.
  • Rectangle: diagonals bisect each other AND are equal in length.
  • Rhombus: diagonals bisect each other AND are perpendicular (meet at 90°).
  • Square: diagonals are equal, perpendicular and bisect each other — all three at once.
  • So the diagonals are a quick test: measure them and see how they meet to name the shape.

Where you'll meet it

Quadrilaterals at work

Building and tiling

Rectangles and squares fill our world — bricks, tiles, windows, screens — because their right angles let pieces fit edge to edge with no gaps. Builders check diagonals are equal to be sure a frame is "true".

Folding gates & linkages

A collapsible gate or a scissor lift is a chain of parallelograms. Because opposite sides stay parallel, the structure can fold and unfold smoothly while staying level.

Design and kites

From kite-shaped signboards to rhombus patterns on fabric, designers choose a quadrilateral for the way its sides and diagonals look and balance — the geometry decides the style.

Check yourself

Competency quiz

Modelled on the competency-based pattern — MCQ, assertion–reason and a case study, testing whether you can use the ideas, not just recall them.

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Interactive built to the OpenMAIC approach (THU-MAIC, MIT). Content from the NCERT Class 8 Ganita Prakash textbook (ncert.nic.in).

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