SOLUTION: X is the midpoint of line ST. Line RX is perpendicular to line ST. Prove: line RS is congruent to line RT. Line RX is perpendicular to line ST: GIVEN <RXS and <RXT are rt. Ang

Algebra ->  Geometry-proofs -> SOLUTION: X is the midpoint of line ST. Line RX is perpendicular to line ST. Prove: line RS is congruent to line RT. Line RX is perpendicular to line ST: GIVEN <RXS and <RXT are rt. Ang      Log On


   

Question 1004104: X is the midpoint of line ST. Line RX is perpendicular to line ST.
Prove: line RS is congruent to line RT.
Line RX is perpendicular to line ST: GIVEN
Line RX is congruent to line RX:?
X is the midpoint of line ST:GIVEN
SX is congruent to TX:?
?: SAS
Line RS is congruent to RT
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Drawing:


The stuff in red is the stuff added
NumberStatementReason
1.Line RX is perpendicular to line STGiven
2.Line RX is congruent to line RXReflexive Property of Congruence
3.X is the midpoint of line STGiven
4.Angle RXS = angle RXTAll perpendicular angles are congruent (and equal to 90 degrees)
5.SX is congruent to TXDefinition of Midpoint (uses line 3)
6.Triangle SRX is congruent to triangle TRXSAS Property of Congruence (uses lines 2,4,5)
7.Line RS is congruent to RTCPCTC


Note:
CPCTC = Corresponding Parts of Congruent Triangles are Congruent