Chapter 5.3, Problem 25PSB

To determine

To Prove: The opposite angles of a parallelogram are congruent.

Explanation of Solution

Given:

  

ABCD as a parallelogram.

Concept Used:

When two parallel lines are intersected by a transversal alternate interior angles are equal

Proof:

Here, we have

  

ABCD as a parallelogram.

Since, when two parallel lines are intersected by a transversal alternate interior angles are equal.

  $\begin{array}{l}\Rightarrow \angle BAC=\angle DCA\\ \Rightarrow \angle DAC=\angle BCA\\ \Rightarrow \angle BAC+\angle DAC=\angle DCA+\angle BCA\\ \Rightarrow m\angle BCD=m\angle DAB\\ \Rightarrow \angle BCD\cong \angle DAB\end{array}$