Question

1. given that △uvt is the mid - segment △, tell which of the following are true. select all that apply. 2(tu)=pn, mn ii uv, 2mp = tv, ut ii vn

Explanation:

Step1: Recall mid - segment theorem

In a triangle, a mid - segment (a line segment joining the mid - points of two sides of a triangle) is parallel to the third side and its length is half of the length of the third side.

Step2: Analyze option A

Since $\triangle UVT$ is a mid - segment triangle, $TU$ is a mid - segment parallel to $PN$. By the mid - segment theorem, $2(TU)=PN$.

Step3: Analyze option B

$MN$ and $UV$ are related in such a way that because $\triangle UVT$ is a mid - segment triangle, $MN\parallel UV$ according to the mid - segment theorem.

Step4: Analyze option C

$MP$ and $TV$ are not related by the mid - segment theorem in the way $2MP = TV$. There is no such relationship based on the mid - segment properties.

Step5: Analyze option D

$UT$ is a mid - segment of a relevant triangle part, and by the mid - segment theorem, $UT\parallel VN$.

Answer:

• A. $2(TU)=PN$
• B. $MN\parallel UV$
• D. $UT\parallel VN$