(Note: We have to assume PXT is a straight line segment or else it
couldn't be true.)
PLAN:
We only have to prove that all three triangles in the
figure are right triangles which have their corresponding angles
congruent. For then Angle S will be congruent to right Angles
4 and 5.
The "main" theorem we will use is:
If two angles of a triangle are congruent to two angles
of another triangle, then the third angles are also congruent.
Angles 4 and 5 are given as right angles and Angle 1 is
Congruent to Angle 2. Therefore by that "main" theorem above,
Angles P and Y are congruent.
Therefore Angle P and Angle T are congruent, for they are both
congruent to Angle Y.
Angles 1 and 3 are congruent because they are vertical angles.
Therefore by the "main" theorem above, Angles 4 and S are
congruent.
Angle 4 is a right angle.
Therefore Angle S is also a right angle, and that proves that
ST is perpendicular to SY.
Edwin
