Chapter 10.2, Problem 5PSA

To determine

To prove: that the $ABCD$ is a parallelogram if $P$ is the mid-point of segment $MN$ .

Answer to Problem 5PSA

  $ABCD$ is a parallelogram.

Explanation of Solution

Given:

  

Concept used:

Alternative interior angles ae congruent.

If the distances from the center of the circle to the chords are congruent, then the chords are congruent.

Opposite sides of a quadrilateral are congruent and parallel.

Calculation:

Here, alternative interior angles ae congruent.

According to the given:

  $c\text{ and }d$ transversal with $MN$ .

Therefore, the line $AD=BC$ .

If the distances from the center of the circle to the chords are congruent, then the chords are congruent.

  $AD=BC$ .

Opposite sides of a quadrilateral are congruent and parallel.

Hence, $ABCD$ is a parallelogram.