Question

pqrs is a parallelogram. \\( \overline { p r } \\) and \\( \overline { q s } \\) are diagonals. match each element to its value.

Explanation:

Step1: Use the property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So, \(a + 4=2a\).
Solve the equation \(a + 4=2a\). Subtract \(a\) from both sides: \(4=2a - a\), so \(a = 4\).

Step2: Use the property of parallelogram diagonals for \(b\)

Also, \(b=2b - 3\). Subtract \(2b\) from both sides: \(b-2b=- 3\), so \(-b=-3\), and \(b = 3\).

Step3: Calculate the length of \(\overline{PR}\)

Since \(a = 4\), \(PR=(a + 4)+2a=(4 + 4)+2\times4=8 + 8=16\).

Step4: Calculate the length of \(\overline{QS}\)

Since \(b = 3\), \(QS=b+(2b - 3)=3+(2\times3 - 3)=3+(6 - 3)=3 + 3=6\).

Answer:

value of \(a\): \(4\), length of \(\overline{PR}\): \(16\), value of \(b\): \(3\), length of \(\overline{QS}\): \(6\)