SOLUTION: Need help on this proof, please. I have to write reasons for the statements of the proof. GIVEN: linePS and lineQT are chords intersecting at R. PROVE: triangleQRP is similiar t

Question 168331: Need help on this proof, please.
I have to write reasons for the statements of the proof.
GIVEN: linePS and lineQT are chords intersecting at R.
PROVE: triangleQRP is similiar to triangleSRT.
STATEMENTS
1. line PS and lineQT are chords intersecting at R. 1. Given.
2. angleQPS is congruent to angleSTQ and anglePQT 2. ????
is congruent to angleTSP. 3. ????
3. triangleQRP is similiar to triangleSRT.
I just need the reasons for numbers 2 and 3. Thanks a bunch!
Answer by stanbon(57250) (Show Source):
You can put this solution on YOUR website!
GIVEN: linePS and lineQT are chords intersecting at R.
PROVE: triangleQRP is similiar to triangle SRT.
STATEMENTS
Comment: Draw the picture so you can see why the reasons are what they are.
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1. line PS and lineQT are chords intersecting at R.
1. Reason: Given.
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2. angle QPS is congruent to angle STQ and
angle PQT is congruent to angleTSP.
2. Reason: Each angle pair subtends the same arc and therefore
mQPS=mSTQ and mPQT=mTSP.
3. angle QRP = angle SRT.
3. Reason : these are vertical angles
4. triangle QRP is similiar to triangle SRT.
4: Reason: three angles of one triangle are correspondingly equal to three angles of the other triangle.
I just need the reasons for numbers 2 and 3.
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Cheers,
Stan H.