Question

examples 3 and 4 cd is the midsegment of trapezoid abgf. 6. if ab = 7 and fg = 11, find cd. 7. if fg = 22 and cd = 13, find ab. 8. if ba = 17 and dc = 32, find cd. 9. if cd = 12 and gf = 13, find ba. 10. if ab = 14.5 and gf = 17.5, find cd.

Explanation:

Step1: Recall mid - segment formula

The formula for the length of the mid - segment $CD$ of a trapezoid $ABGF$ is $CD=\frac{AB + FG}{2}$.

Step2: Solve problem 6

Given $AB = 7$ and $FG=11$, substitute into the formula: $CD=\frac{7 + 11}{2}=\frac{18}{2}=9$.

Step3: Solve problem 7

We know $CD=\frac{AB + FG}{2}$, so $2CD=AB + FG$, and $AB = 2CD−FG$. Substitute $FG = 22$ and $CD = 13$: $AB=2\times13−22=26 - 22 = 4$.

Step4: Solve problem 8

There is a confusion as $BA$ and $DC$ are likely mis - labeled. Assuming the correct formula $CD=\frac{AB + FG}{2}$, if $AB = 17$ and $FG$ is not given but we assume $DC$ is a wrong label for $FG$ and $FG = 32$, then $CD=\frac{17+32}{2}=\frac{49}{2}=24.5$.

Step5: Solve problem 9

Using $CD=\frac{AB + FG}{2}$, we can rewrite it as $2CD=AB + FG$, so $AB=2CD−FG$. Substitute $CD = 12$ and $FG = 13$: $AB=2\times12−13=24 - 13 = 11$.

Step6: Solve problem 10

Substitute $AB = 14.5$ and $FG = 17.5$ into $CD=\frac{AB + FG}{2}$: $CD=\frac{14.5+17.5}{2}=\frac{32}{2}=16$.

Answer:

1. $9$
2. $4$
3. $24.5$
4. $11$
5. $16$