Question

Given: Rectangle $\text{QRST}$; $▱\text{RKST}$; $▱\text{JQST}$

Prove: $\overline{\text{JT}}\cong \overline{\text{KS}}$.

Short answer

$\overline{\text{JT}}\cong \overline{\text{KS}}$

Step-by-step solution

Step 1. State the concept used.

Diagonals of rectangles are equal and bisect each other.

The opposite sides of a parallelogram are equal.

Step 2. State the 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 the rectangle are equal to each other, it can be said that, $\overline{TR}\cong \overline{QS}$.

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

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

Step 3. State the conclusion.

Therefore, $\overline{JT}\cong \overline{KS}$(proved).