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