Question

if $pr = 4w - 52$ and $pt = 3w - 29$, find the value of $w$ that makes quadrilateral $qrst$ a parallelogram.
$w = \square$

Explanation:

Step1: Recall parallelogram diagonal property

In a parallelogram, diagonals bisect each other, so $PT = \frac{1}{2}PR$.

Step2: Substitute given expressions

$$3w - 29 = \frac{1}{2}(4w - 52)$$

Step3: Simplify right-hand side

$$3w - 29 = 2w - 26$$

Step4: Isolate w variable

Subtract $2w$ from both sides: $w - 29 = -26$
Add 29 to both sides: $w = -26 + 29$

Answer:

$3$