Write a proof to show that opposite angles of a parallelogram are congruent. be sure to create and name the appropriate geometric figures. this figure does not need to be submitted

1. A parallelogram is formed by 2 pair of parallel line segments intersecting each other.

2. Check Parallelogram ABCD in the atached figure.

3. Since AD is parallel to BC, angles BAC and ACD are alternate interior angles (angles Z), and their measure is equal, say alpha degrees, as shown in the figure.

Similarly m(DAC)=m(BCA)=beta

4. m(A)=m(C)= alpha + beta

5. Conclusion: the measures of 2 opposite angles of a parallelogram are equal.

so "opposite angles of a parallelogram are congruent. "