Question

find the measurement indicated in each parallelogram.

1. dm = 4x - 4

mf = 2x + 10
find df
(there is a parallelogram diagram with vertices f, e, d, c and diagonals intersecting at m)

1. gn = 6x

ge = 11x
find ge

Explanation:

Step1: Recall parallelogram diagonal property

In a parallelogram, the diagonals bisect each other. So \( DM = MF \).
Set \( 4x - 4 = 2x + 10 \).

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides: \( 4x - 2x - 4 = 10 \)
Simplify: \( 2x - 4 = 10 \)
Add 4 to both sides: \( 2x = 10 + 4 \)
\( 2x = 14 \)
Divide by 2: \( x = 7 \).

Step3: Find \( DM \) and \( MF \)

Substitute \( x = 7 \) into \( DM = 4x - 4 \): \( DM = 4(7) - 4 = 28 - 4 = 24 \).
Since \( DM = MF \), \( MF = 24 \).

Step4: Find \( DF \)

\( DF = DM + MF = 24 + 24 = 48 \).

Answer:

\( DF = 48 \)