Chapter 5.1, Problem 29WE

To determine

To Prove: that $\overrightarrow{SJ}=\overrightarrow{QK}$ shown in figure if $\overrightarrow{PJ}\cong \overrightarrow{RK}$ .

Explanation of Solution

Given A $▱PQRS$ and $\overrightarrow{PJ}\cong \overrightarrow{RK}$

and figure is.

  

Proof:

Using two-column.

  $\begin{array}{cc}\text{Statement}& \text{Reason}\\ \overline{SP}\cong \overline{QR}& \text{Opposite sides are congruent in parallelogram}\\ \angle P\cong \angle R& \text{Opposite angles are congruent in parallelogram}\\ \overline{PJ}\cong \overline{RK}& \text{Given}\\ \Delta SPJ\cong \Delta QRK& SAS\text{Postulate}\\ \overrightarrow{SJ}=\overrightarrow{QK}& \text{By CPCT}\end{array}$ .

Therefore, $\overrightarrow{SJ}=\overrightarrow{QK}$ has been proved.