Theorem Of Parallelograms

Theorem 2

In a parallelogram, opposite sides are equal.

Theorem 2
In a parallelogram, opposite sides are equal.

Given:
A parallelogram ABCD.

To Prove: AB=DC and BC=AD

Construction: Join AC.


Proof:

Statements
Reasons
In △ABC and △ CDA
1. ∠BAC=∠ACD 1. Alternate ∠s, AB ∥ DC and AC is transversal
2. ∠BCA=∠CAD 2. Alt, ∠s, BC∥AD and AC is transversal.
3. AC=CA
3. Common
4. △ABC △CDA 4. ASA Congruency.
5. AB= DC and BC=AD
5. c.p.c.t.

The converse of the above theorem is also true. i.e. In a quadrilateral if opposite sides are equal, it is a parallelogram.