Chapter 6.3, Problem 5CYP

To determine

To calculate: To write a coordinate proof of the statement

Answer to Problem 5CYP

It is proved thatif a quadrilateral is a parallelogram, then opposite sides are congruent

Explanation of Solution

Given: Statement is “If a quadrilateral is a parallelogram, then opposite sides are congruent”

Formula Used:

In a parallelogram, opposite sides are equal

Two figures are congruent when the figures have same shape and size

Calculation:

Given that $▱HJKP$ is a parallelogram

Here, HJ and PK are opposite sides

And opposite sides of parallelogram are parallel and equal

  $HJ\parallel PK$ and $HJ=PK$

Thus, $\overline{HJ}\cong \overline{PK}$

Hence,

Conclusion:

Hence, proved that if a quadrilateral is a parallelogram, then opposite sides are congruent