if c, p, and t are the midpoints of the sides of $ \triangle aen, pt = 13, en = 43 $, and $ cp = 29 $, find each measure.
1) $ ae = $
2) $ an = $
3) $ ct = $
4) perimeter of $ \triangle aen = $

Question

Accepted Answer

# Explanation:
## Step1: Use the mid - segment theorem
The mid - segment theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.
Since $C$ and $P$ are midpoints of $AE$ and $EN$ respectively, $CP\parallel AN$ and $CP=\frac{1}{2}AN$.
Given $CP = 29$, then $AN=2\times CP$.
$AN = 2\times29=58$
Since $P$ and $T$ are midpoints of $EN$ and $WN$ respectively, $PT\parallel AE$ and $PT=\frac{1}{2}AE$.
Given $PT = 13$, then $AE=2\times PT$.
$AE = 2\times13 = 26$
Since $C$ and $T$ are midpoints of $AE$ and $AN$ respectively, $CT\parallel EN$ and $CT=\frac{1}{2}EN$.
Given $EN = 43$, then $CT=\frac{1}{2}\times43=21.5$

## Step2: Calculate the perimeter of $\triangle AEN$
The perimeter of $\triangle AEN$ is $P=AE + EN+AN$.
Substitute $AE = 26$, $EN = 43$, and $AN = 58$ into the formula.
$P=26 + 43+58=127$

# Answer:
1. $AE = 26$
2. $AN = 58$
3. $CT = 21.5$
4. Perimeter of $\triangle AEN=127$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the mid - segment theorem

Step2: Calculate the perimeter of \(\triangle AEN\)

Answer: