Question

Prove <1 is congruent to <2

Answer 1

Given that \[\frac{ PR }{ MR} = \frac{ QR }{ NR} \]

Answer 2

hint:
starting from your condition, we can write:
\[\begin{gathered}
\frac{{MR}}{{PR}} = \frac{{NR}}{{QR}} \hfill \\
\left( {MR - PR} \right):PR = \left( {NR - QR} \right):NR \hfill \\
MP:PR = NQ:NR \hfill \\
\end{gathered} \]

Answer 3

Now we can apply the theorem of Talete. What can we conclude?