name all the points shown that must be midpoints of the sides of the large triangle.
7.
8.
9.
$\overleftrightarrow{ae}$, $\overleftrightarrow{bf}$, $\overleftrightarrow{cg}$, and $\overleftrightarrow{dh}$ are parallel, with $ef = fg = gh$. complete.
10. if $ab = 5$, then $ad = \underline{\ ?\ }$.
11. if $ac = 12$, then $cd = \underline{\ ?\ }$.
12. if $ab = 5x$ and $bc = 2x + 12$, then $x = \underline{\ ?\ }$.
13. if $ac = 22 - x$ and $bd = 3x - 22$, then $x = \underline{\ ?\ }$.
b 14. if $ab = 15$, $bc = 2x - y$, and $cd = x + y$, then $x = \underline{\ ?\ }$ and $y = \underline{\ ?\ }$.
15. if $ab = 12$, $bc = 2x + 3y$, and $bd = 8x$, then $x = \underline{\ ?\ }$ and $y = \underline{\ ?\ }$.

Question

Accepted Answer

# Explanation:
## Step1: Analyze the parallel lines and equal segments
Given that $\overleftrightarrow{AE}$, $\overleftrightarrow{BF}$, $\overleftrightarrow{CG}$, and $\overleftrightarrow{DH}$ are parallel, and $EF = FG = GH$. By the Basic Proportionality Theorem (Thales' theorem) or the theorem of parallel lines cutting transversals proportionally, the segments on the transversal $AD$ should be equal. Since there are three equal segments on the other transversal ($EF, FG, GH$), the transversal $AD$ is divided into three equal parts as well. So $AB = BC = CD$.

## Step2: Solve for $AD$ when $AB = 5$
Since $AB = BC = CD = 5$ (from the proportionality of parallel lines), then $AD=AB + BC+CD$. Substituting the values, we get $AD = 5+5 + 5=15$.

# Answer:
$15$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Analyze the parallel lines and equal segments

Step2: Solve for \(AD\) when \(AB = 5\)

Answer: