Class 9 - Mathematics - Ten Parallelogram Theorems You Must Know (#cbsenotes)(#eduvictors)

10 Parallelogram Theorems - You Must Know

Theorem 1: A diagonal of a parallelogram divides it into two congruent triangles.

See proof here. 

Theorem 2: In a parallelogram, opposite sides are equal.
See proof here. 

Theorem 3: If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.
See proof here. 

Theorem 4: In a parallelogram, opposite angles are equal
See proof here. 

Theorem 5: If each pair of opposite angles of a quadrilateral is equal, then it is a parallelogram.
See proof here. 

Theorem 6: If a pair of opposite sides of a quadrilateral is equal and parallel, then it is a parallelogram.
See proof here. 

Theorem 7: If a pair of opposite sides of a quadrilateral is equal and parallel, then it is a parallelogram.
See proof here. 

Theorem 8: If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
See proof here. 

Theorem 9: Mid-point theorem

The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is equal to half of it.
See proof here. 

Theorem 10: Converse of mid-point theorem

The line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.
See proof here. 

☛See also:
CH 8 Quadrilaterals
CH 8 Quadrilaterals (NCERT Ex 8.1)
CH 8 Quadrilaterals (NCERT Ex 8.2)
CH 8 Quadrilaterals (Important Points To Remember)
CH 8 Quadrilaterals (Problems and Solutions)
CH 8 Quadrilateral (Worksheet)
Understanding Quadrilaterals (Worksheet)
Understanding Quadrilaterals (MCQs)
10 Parallelogram Theorems You Must Know!