Questions: Find TX. TX=

Find TX. 
TX=
Transcript text: Find $T X$. \[ T X= \]
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Solution

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Solution Steps

Step 1: Identify the given information

We are given that $VX = 34$, $UT = 17$, and $WT$ is parallel to $VU$. We want to find the length of $TX$.

Step 2: Use the Triangle Midsegment Theorem

Since $WT$ is parallel to $VU$, $WT$ is the midsegment of $\triangle VUX$. The Triangle Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side. Therefore, $WX = \frac{1}{2} VX$.

Step 3: Calculate WX

$WX = \frac{1}{2} \times VX = \frac{1}{2} \times 34 = 17$.

Step 4: Determine the relationship between WX and VX

$VX = WX + TX$. We have $VX = 34$ and $WX = 17$.

Step 5: Calculate TX

$TX = VX - WX = 34 - 17 = 17$.

Final Answer

\\(\boxed{TX = 17}\\)

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