Theorem Of Parallelograms

Theorem 4

In a parallelogram, opposite angles are equal.

Theorem:
In a parallelogram, opposite angles are equal.


Given:A parallelogram ABCD.
To prove: ∠A=∠C and ∠B=∠D.

Proof:
Statements
Reasons
1. ∠A+∠B=180° 1.AD∥BC and AB is a transversal, sum of co-interior angles=180°
2.∠B=∠C=180° 2. AB∥DC and BC is a transversal, sum of co-interior angles=180°
3.∠A+∠B=∠B+∠C
⇒ ∠A=∠C
Similarly, ∠B = ∠D.
From 1 and 2