Question

1. given that δuvt is the mid - segment δ, tell which of the following are true. ○δtuv≅δutm ○δtuv≅δpvu ○δtuv≅δvnt ○ all of the above 5.4

Explanation:

Step1: Recall mid - segment properties

A mid - segment of a triangle is parallel to a side of the triangle and half its length. Since \(\triangle UVT\) is a mid - segment triangle, we can use congruence criteria.

Step2: Analyze \(\triangle TUV\cong\triangle UTM\)

By Side - Angle - Side (SAS) or other congruence postulates. We can show that corresponding sides and angles are equal due to mid - segment relationships and parallel lines (which give equal angles).

Step3: Analyze \(\triangle TUV\cong\triangle PVU\)

Again, using properties of mid - segments, parallel lines and equal distances between parallel lines, we can find equal sides and angles to satisfy a congruence postulate like SAS.

Step4: Analyze \(\triangle TUV\cong\triangle VNT\)

With mid - segment properties, we can establish equal side lengths and angle measures to show congruence by a congruence postulate such as SAS. So all the given congruences are true.

Answer:

All of the above