Q1. In triangle ABC, D and E are the midpoints of AB and AC. If BC = 10 cm, find DE.
By the midpoint theorem, DE is parallel to BC and half its length.
DE = ½ × BC = ½ × 10
DE = 5 cm
Quadrilaterals — Class 9
A parallelogram hides several neat properties, and the midpoint theorem is one of the most useful shortcuts in geometry.
Parallelogram propertiesOpposite sides are equal and parallel; opposite angles are equal; diagonals bisect each other.
Midpoint theoremThe line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
Special parallelogramsRectangle (all angles 90°), rhombus (all sides equal), square (both).
Solved examples
Formula sheet
| Quantity | Formula |
|---|---|
| Midpoint theorem | DE ∥ BC, DE = ½ BC |
| Diagonals of a parallelogram | bisect each other |
| Angle sum of a quadrilateral | 360° |
Common mistakes & exam wins
- A quadrilateral is a parallelogram if any ONE of: opposite sides equal, opposite angles equal, diagonals bisect each other, or one pair of sides is both equal and parallel.
- The midpoint theorem works only for the segment joining midpoints of TWO sides of a triangle.
- All four angles of any quadrilateral always add up to 360°.
Frequently asked questions
What is the midpoint theorem?
The segment joining the midpoints of two sides of a triangle is parallel to the third side and equal to half of it.
What are the properties of a parallelogram?
Opposite sides are equal and parallel, opposite angles are equal, and the diagonals bisect each other.
What is the sum of the interior angles of a quadrilateral?
360°, for any quadrilateral.