Properties_of_Trapezium. Class 7-10 maths

Quadrilateral

1. Properties of Trapezium Class 9 Mathematics - Understanding Trapezium

2. What is a Trapezium? A trapezium (or trapezoid) is a quadrilateral with at least one pair of opposite sides parallel.

3. Types of Trapezium 1. **Scalene Trapezium** - No sides are equal. 2. **Isosceles Trapezium** - Non-parallel sides are equal. 3. **Right-angled Trapezium** - Has one right angle.

4. Basic Properties 1. One pair of opposite sides is parallel. 2. Sum of the interior angles is always 360°. 3. Adjacent angles on the same side of a non-parallel side are supplementary.

5. Properties of Isosceles Trapezium 1. Non-parallel sides are equal. 2. Base angles are equal. 3. Diagonals are of equal length.

6. Properties of Right-Angled Trapezium 1. One of the non-parallel sides is perpendicular to the bases. 2. One angle is 90°. 3. The height of the trapezium is equal to the perpendicular side.

7. The Mid-Segment (Median) Theorem The line joining the midpoints of the non-parallel sides is called the median. Property: The median is parallel to the bases and equal to their average length: **Median = (Base1 + Base2) / 2**.

8. Area of a Trapezium Formula: **Area = 1/2 × (Sum of Parallel Sides) × Height** Example: If bases are 8 cm and 12 cm, and height is 5 cm, Area = 1/2 × (8+12) × 5 = 50 cm².

9. Example Problem A trapezium has bases 10 cm and 6 cm, and height 4 cm. Find its area. Solution: Area = 1/2 × (10+6) × 4 = 32 cm².

10. Conclusion • Trapeziums have one pair of parallel sides. • Different types have unique properties. • Important for solving geometry problems involving height, angles, and area.