Question

question 3 (mcas) parallelogram pqrs, its diagonals, and expressions representing some of its angle measures are shown in this diagram. the diagonals of the parallelogram intersect at point t. part a based on the diagram, which of the following statements is not true? ① pq = sr ② pt = rt ③ pr = sq ④ ps = qr part b which of the following is the value of x in the diagram ① x = 2/3 ② x = 3/2 ③ x = 8/33 ④ x = 33/8

Explanation:

Step1: Recall properties of parallelogram

In a parallelogram, opposite sides are congruent and diagonals bisect each other. Opposite sides $PQ = SR$, $PS=QR$ and diagonals bisect each other so $PT = RT$. But diagonals of a parallelogram are not necessarily equal, so $PR
eq SQ$ in general. So for Part A, the statement that is not true is $PR = SQ$.

Step2: Use angle - congruence property

In parallelogram $PQRS$, $\angle PST=\angle TQR$ (alternate - interior angles). So $45x=21x + 16$.

Step3: Solve the equation for $x$

Subtract $21x$ from both sides: $45x-21x=21x + 16-21x$.
$24x=16$.
Then divide both sides by 24: $x=\frac{16}{24}=\frac{2}{3}$.

Answer:

Part A: C. $PR = SQ$
Part B: A. $x=\frac{2}{3}$