What theorem shows that TPN ≅ TQM?

Triangles T Q M and T P N which share vertex T. Side T A in the first triangle is congruent to side T P in the second triangle. Side T M in the first triangle is congruent to side T N in the second. The angles at vertex T are vertical angles and are included between the two pairs of congruent sides.

Group of answer choices

AAS

ASA

SAS

SSS

Answers

Answer 1

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.


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