Note: Consider the side of first triangle is TQ instead of TA.
Given:
Triangles TQM and TPN which share vertex T.
[tex]TQ\cong TP,TM\cong TN[/tex]
To find:
The theorem which shows that [tex]\Delta TPN\cong TQM[/tex].
Solution:
In triangle TQM and TPN,
[tex]TQ\cong TP[/tex] [Given]
[tex]\angle QTM\cong \angle PTN[/tex] [Given]
[tex]TM\cong TN[/tex] [Given]
Since two sides and their including angle are congruent in both triangles, therefore both triangles are congruent by SAS postulate.
[tex]\Delta TPN\cong TQM[/tex] [SAS]
Therefore, the correct option is C.
