Question

1. given that δuvt is the midsegment 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 property

A mid - segment of a triangle is parallel to the third side and half its length. In the context of congruence, we use side - angle - side (SAS), angle - side - angle (ASA), etc. criteria.

Step2: Analyze $\triangle TUV\cong\triangle ATM$

We can show congruence by using properties of mid - segments and parallel lines to get equal angles and equal side lengths (by mid - point and mid - segment relationships) to satisfy a congruence criterion like ASA or SAS.

Step3: Analyze $\triangle TUV\cong\triangle PVU$

Again, using properties of parallel lines (due to mid - segment being parallel to a side) and mid - point properties, we can find equal angles and equal side lengths to satisfy a congruence criterion.

Step4: Analyze $\triangle TUV\cong\triangle VNT$

Similar to above, by leveraging the mid - segment characteristics such as parallel lines and mid - point relationships, we can establish congruence using appropriate congruence postulates.

Answer:

All of the above