Question

pqrs is a parallelogram. $overline{pr}$ and $overline{qs}$ are diagonals. match each element to its value. value of a length of $overline{pr}$ value of b length of $overline{qs}$ 16 4 3 6

Explanation:

Step1: Use diagonal - bisecting property

In a parallelogram, the diagonals bisect each other. So, $PT = TR$ and $QT=TS$.
We have $a + 4=2a$ and $b=2b - 3$.

Step2: Solve for $a$

From $a + 4=2a$, subtract $a$ from both sides: $4=2a - a$, so $a = 4$.

Step3: Solve for $b$

From $b=2b - 3$, subtract $b$ from both sides and add 3 to both sides: $3=2b - b$, so $b = 3$.

Step4: Calculate length of $\overline{PR}$

Since $PR=PT + TR$ and $PT=a + 4$, $TR = 2a$, when $a = 4$, $PT=4 + 4=8$ and $TR = 2\times4=8$, so $PR=8 + 8=16$.

Step5: Calculate length of $\overline{QS}$

Since $QS=QT + TS$ and $QT = b$, $TS=2b - 3$, when $b = 3$, $QT = 3$ and $TS=2\times3 - 3=3$, so $QS=3 + 3=6$.

Answer:

Value of $a$: 4
Length of $\overline{PR}$: 16
Value of $b$: 3
Length of $\overline{QS}$: 6