Question

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

Explanation:

Step1: Since EF bisects CD, then CG = GD

Set up the equation $5x - 1=7x - 13$.

Step2: Solve the equation for x

Subtract $5x$ from both sides: $- 1=2x - 13$. Then add 13 to both sides: $12 = 2x$. Divide both sides by 2, so $x = 6$.

Step3: Find the length of EF

Substitute $x = 6$ into the expression for EF. $EF=6x - 4=6\times6 - 4=36 - 4 = 32$.

Step4: Find EG

Since $EG=EF + GF$ and $GF = 13$, then $EG=32+13=45$.

Answer:

45