Question

allelogram proofs quick check formal proofs if you were to prove that quadrilateral abcd is a parallelogram, what would need to be true about eb and ed

Explanation:

Step1: Recall the property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So, if \(ABCD\) is a parallelogram, then \(EB = ED\).

Step2: Set up the equation

Since \(EB=8 + z\) and \(ED = 15 - z\), and \(EB = ED\), we have the equation \(8 + z=15 - z\).

Step3: Solve the equation for \(z\)

Add \(z\) to both sides: \(8 + z+z=15 - z+z\), which simplifies to \(8 + 2z=15\).
Subtract \(8\) from both sides: \(2z=15 - 8\), so \(2z = 7\).
Divide both sides by \(2\): \(z=\frac{7}{2}=3.5\).
Then \(EB=8 + 3.5 = 11.5\) and \(ED=15 - 3.5 = 11.5\).

Answer:

\(EB = ED\) (because in a parallelogram, diagonals bisect each other)