- Theorem - A diagonal of a parallelogram divides it into two congruent triangles
- Theorem - In a parallelogram, opposite sides are equal
- Theorem - If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram
- Theorem - In a parallelogram, opposite angles are equal
- Theorem - If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram
- Theorem - The diagonals of a parallelogram bisect each other
- Theorem - If the diagonals of a quadrilateral bisect each other, then it is a parallelogram
The sides AB and CD of a parallelogram ABCD are bisected at E and F. Prove that EBFD is a parallelogram.
In Fig. below, AB = AC and CP || BA and AP is the bisector of exterior ∠CAD of ΔABC.
Prove that (i) ∠PAC = ∠BCA (ii) ABCP is a parallelogram
P and Q are the points of trisection of the diagonal BD of a parallelogram AB Prove that CQ is parallel to AP. Prove also that AC bisects PQ.
In Fig., below, ABCD is a parallelogram in which ∠A = 60°. If the bisectors of ∠A and ∠B meet at P, prove that AD = DP, PC = BC and DC = 2AD.