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Class 9 Quadrilaterals: cheat sheet
CBSE Mathematics. The properties of parallelograms, rectangles, rhombuses and squares, and the mid-point theorem for triangles.
Key ideas
- The angles of any quadrilateral add up to 360°.
- In a parallelogram, opposite sides are equal, opposite angles are equal, and the diagonals bisect each other.
- Neighbouring angles of a parallelogram add up to 180°.
- A rectangle is a parallelogram with equal diagonals; a rhombus has diagonals that bisect each other at right angles.
- A square has all of these: equal sides, right angles, and equal diagonals at right angles.
- Mid-point theorem: the line joining the midpoints of two sides of a triangle is parallel to the third side and half as long.
Remember
| Angle sum | ∠A + ∠B + ∠C + ∠D = 360° |
| Parallelogram | ∠A + ∠B = 180° (neighbouring angles) |
| Mid-point theorem | DE ∥ BC and DE = ½ BC |
| Triangle of midpoints | perimeter = ½ × perimeter of the original |
Watch out
- Assuming a rhombus has equal diagonals (only if it is a square).
- Saying the diagonals of every parallelogram are perpendicular.
- Doubling instead of halving in the mid-point theorem.
Worked example
The sides of a triangle are 21 cm, 26 cm and 8 cm. Find the perimeter of the triangle formed by joining the mid-points of its sides.
Working: each side of the new triangle is half a side of the old one: 55 ÷ 2
Answer: 27.5 cm
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