Question

if pt = 2z and rt = z + 11, find the value of z that makes quadrilateral pqrs a parallelogram.

Explanation:

Step1: Recall parallelogram diagonals property

In a parallelogram, the diagonals bisect each other. So, \( PT = RT \).

Step2: Set up the equation

Given \( PT = 2z \) and \( RT = z + 11 \), we set them equal: \( 2z = z + 11 \).

Step3: Solve for z

Subtract \( z \) from both sides: \( 2z - z = z + 11 - z \), which simplifies to \( z = 11 \).

Answer:

\( 11 \)