Math  /  Geometry

QuestionCheating Challenge in Sims 4 - Youlude Complete the proof that PTVRUS\triangle P T V \cong \triangle R U S. \begin{tabular}{|c|c|c|c|c|} \hline & Statement & \multicolumn{3}{|l|}{Reason} \\ \hline 1 & PTVRUS\angle P T V \cong \angle R U S & Given & & \\ \hline 2 & STUV\overline{S T} \cong \overline{U V} & Given & & \\ \hline 3 & PR\angle P \cong \angle R & Given & & \\ \hline 4 & TV=UV+TUT V=U V+T U & & & - \\ \hline 5 & SU=ST+TUS U=S T+T U & Additive & & \\ \hline 6 & TV=ST+TUT V=S T+T U & & & \\ \hline 7 & SU=TVS U=T V & Transitiv & & \\ \hline 8 & PTVRUS\triangle P T V \cong \triangle R U S & & - & \\ \hline \end{tabular}

Studdy Solution
Conclude triangle congruence using the SAS postulate:
Since we have two pairs of congruent angles and one pair of congruent sides between the triangles, we can conclude:
PTVRUS\triangle P T V \cong \triangle R U S
The triangles PTV\triangle P T V and RUS\triangle R U S are congruent by the Side-Angle-Side (SAS) postulate.

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