Question

drag the tiles to the correct boxes to complete the pairs.
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: Solve for $a$ (diagonals bisect)

In a parallelogram, diagonals bisect each other, so $a+4=2a$.
Rearrange: $2a - a = 4$ → $a=4$

Step2: Calculate length of $\overline{PR}$

$\overline{PR}=(a+4)+2a$. Substitute $a=4$:
$\overline{PR}=(4+4)+2(4)=8+8=16$

Step3: Solve for $b$ (diagonals bisect)

Diagonals bisect each other, so $b=2b-3$.
Rearrange: $2b - b = 3$ → $b=3$

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

$\overline{QS}=b+(2b-3)$. Substitute $b=3$:
$\overline{QS}=3+(2(3)-3)=3+3=6$

Answer:

16 → length of $\overline{PR}$
4 → value of $a$
3 → value of $b$
6 → length of $\overline{QS}$