Question

1. if ef bisects cd, cg = 5x - 1, gd = 7x - 13, ef = 6x - 4, and gf = 13, find eg.

Explanation:

Step1: Use the bisect property

Since \( EF \) bisects \( CD \), \( CG = GD \). So we set up the equation:
\( 5x - 1 = 7x - 13 \)

Step2: Solve for \( x \)

Subtract \( 5x \) from both sides:
\( -1 = 2x - 13 \)
Add 13 to both sides:
\( 12 = 2x \)
Divide by 2:
\( x = 6 \)

Step3: Find \( EF \)

Substitute \( x = 6 \) into \( EF = 6x - 4 \):
\( EF = 6(6) - 4 = 36 - 4 = 32 \)

Step4: Find \( EG \)

We know \( EF = EG + GF \), and \( GF = 13 \). So \( EG = EF - GF \):
\( EG = 32 - 13 = 19 \)

Answer:

\( 19 \)