Question

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

Explanation:

Step1: Recall mid - segment theorem

In a triangle, a mid - segment is parallel to the third side and its length is half of the third side.

Step2: Analyze $2(TU)=PN$

Since $\triangle UVT$ is a mid - segment triangle, $TU$ is parallel to $PN$ and $TU=\frac{1}{2}PN$, so $2(TU)=PN$.

Step3: Analyze $MN\parallel UV$

By the mid - segment theorem, the mid - segment of a triangle is parallel to the side of the larger triangle it doesn't touch. Here, $UV$ is a mid - segment and is parallel to $MN$.

Step4: Analyze $2MP = TV$

There is no mid - segment relationship that implies $2MP = TV$.

Step5: Analyze $UT\parallel VN$

As $\triangle UVT$ is a mid - segment triangle, $UT$ is parallel to $VN$ according to the mid - segment theorem.

Answer:

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