Question

a) find the measurement indicated in each parallelogram.
b) justify your answer with an appropriate parallelogram property.

1. bd = 24

id = 3x - 6

1. xa = 22

az = 21x + 1
(handwritten notes: diagonals bisect each other, 3x - 6 = 12, 3x = 18, x = 6; diagonals bisect each other, 21x + 1...)
(diagrams of parallelograms included)

Explanation:

Step1: Use parallelogram diagonal property

In a parallelogram, diagonals bisect each other, so $BD = 2 \times OD$. Thus:
$24 = 2(3x - 6)$

Step2: Solve for x

Divide both sides by 2:
$12 = 3x - 6$
Add 6 to both sides:
$18 = 3x$
Divide by 3:
$x = 6$

Step3: Use parallelogram diagonal property

In a parallelogram, diagonals bisect each other, so $XA = AZ$. Thus:
$22 = 21x + 1$

Step4: Solve for x

Subtract 1 from both sides:
$21 = 21x$
Divide by 21:
$x = 1$

Answer:

For 53): $x = 6$
For 54): $x = 1$