Math  /  Geometry

QuestionMb Apbs (1015) YouTube bal 00 m/math/00 \mathrm{~m} / \mathrm{math} / geometry/proving-triangles-congruent-by-sss-sas-asa-and-aas Complete the proof that PRTPSQ\triangle P R T \cong \triangle P S Q. \begin{tabular}{|l|l|l|} \hline & Statement & Reason \\ \hline 1 & SPTQPR\angle S P T \cong \angle Q P R & Given \\ \hline 2 & PSPR\overline{P S} \cong \overline{P R} & Given \\ \hline 3 & PSQPRT\angle P S Q \cong \angle P R T & Given \\ \hline 4 & mRPT=mRPS+mSPTm \angle R P T=m \angle R P S+m \angle S P T & \\ \hline 5 & mQPS=mQPR+mRPSm \angle Q P S=m \angle Q P R+m \angle R P S & Additive Property of Angle Measure \\ \hline 6 & mRPT=mRPS+mQPRm \angle R P T=m \angle R P S+m \angle Q P R & Substitution \\ \hline 7 & mQPS=mRPTm \angle Q P S=m \angle R P T & \\ \hline 8 & PRTPSQ\triangle P R T \cong \triangle P S Q & \\ \hline \end{tabular} Sign out Nev 15

Studdy Solution
Conclude the congruence of triangles using the Angle-Side-Angle (ASA) postulate:
- We have: PSQPRT\angle PSQ \cong \angle PRT (Given) PSPR\overline{PS} \cong \overline{PR} (Given) QPSRPT\angle QPS \cong \angle RPT (Proven)
- By the ASA postulate, PRTPSQ\triangle PRT \cong \triangle PSQ.
The triangles are congruent:
PRTPSQ \boxed{\triangle PRT \cong \triangle PSQ}

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