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 to find x

Since \( EF \) bisects \( CD \), \( CG = GD \). So we set up the equation:
\( 5x - 1 = 7x - 13 \)
Subtract \( 5x \) from both sides:
\( -1 = 2x - 13 \)
Add 13 to both sides:
\( 12 = 2x \)
Divide both sides by 2:
\( x = 6 \)

Step2: Find the length of \( EF \)

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

Step3: Find \( EG \) using \( EF = EG + GF \)

We know \( EF = 32 \) and \( GF = 13 \). Let \( EG = y \), then:
\( y + 13 = 32 \)
Subtract 13 from both sides:
\( y = 32 - 13 = 19 \)

Answer:

\( 19 \)