Question

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

Explanation:

Step1: Use the property of a bisector

Since $\overline{EF}$ bisects $\overline{CD}$, we know that $CG = GD$. So we 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, we get $x = 6$.

Step3: Find the length of $EF$

We know that $EF=6x - 4$. Substitute $x = 6$ into the expression: $EF=6\times6 - 4=36 - 4 = 32$.

Step4: Find the length of $EG$

Since $EF$ bisects $CD$ at $G$ and $GF = 13$, and $EF=EG + GF$. Then $EG=EF - GF$. Substitute $EF = 32$ and $GF = 13$ into the formula, we get $EG=32 - 13=19$.

Answer:

$19$