Question

What theorem shows that TPN ≅ TQM?

Answer 1

Note: Consider the side of first triangle is TQ instead of TA.

Given:

Triangles TQM and TPN which share vertex T.

$TQ\cong TP,TM\cong TN$

To find:

The theorem which shows that $\Delta TPN\cong TQM$.

Solution:

In triangle TQM and TPN,

$TQ\cong TP$        [Given]

$\angle QTM\cong \angle PTN$         [Given]

$TM\cong TN$        [Given]

Since two sides and their including angle are congruent in both triangles, therefore both triangles are congruent by SAS postulate.

$\Delta TPN\cong TQM$              [SAS]

Therefore, the correct option is C.