Chapter 5.4, Problem 31WE

To determine

To prove: $\overline{JT}\cong \overline{KS}$

Explanation of Solution

Given:

Rectangle QRST and parallelogram $▱RKST$ and parallelogram $▱JQST$

Concept used:

Diagonals of rectangles are equal and bisect each other.

The opposite sides of a parallelogram are congruent.

Proof:

Construct a rectangle QRST and parallelogram $▱RKST$ with parallelogram $▱JQST$

  

In parallelogram $▱RKST$ , RT and SK are opposite sides which are parallel, therefore, $\overline{RT}\cong \overline{SK}$

Similarly, in parallelogram $▱JQST$ , JT and QS are opposite sides which are parallel, therefore, $\overline{JT}\cong \overline{QS}$ .

Now, in rectangle QRST, TR and QS are diagonal of the rectangle and as the diagonal of rectangle are equal t each other, we can say that, $\overline{TR}\cong \overline{QS}$ .

From above three relations by the property of transitivity of congruence, $\overline{JT}\cong \overline{KS}$ .

Hence, $\overline{JT}\cong \overline{KS}$