Chapter 6.3, Problem 44HP

To determine

Whether JBKD is a parallelogram.

Answer to Problem 44HP

JBKD is a parallelogram as its diagonals bisect each other.

Explanation of Solution

Given:

ABCD is a parallelogram.

  $\overline{AJ}\cong \overline{KC}$

Calculation:

Draw a line segment BD in the given figure. Label it as P.

As, ABCD is a parallelogram, P is the midpoint of line segments BD and CA.

As, $\overline{AJ}\cong \overline{KC}$ , according to Segment Addition Postulate;

  $\begin{array}{l}JP=AP-AJ\\ JP=PC-PK\\ JP=PK\end{array}$

Therefore, P is also the midpoint of line segment JK. Hence, the diagonals of JBKD bisect each other. And if the diagonals of a quadrilateral bisect each other, it is a parallelogram.

Hence, JBKD is a parallelogram.