Final answer:
The triangle RTW is isosceles because it has two congruent angles (right angles) and one congruent side shared by both sides (RT and TW).
Step-by-step explanation:
Given:
Circle P with diameter RS perpendicular to TW.
To prove:
Triangle RTW is isosceles.
Proof:
Since RS is the diameter of circle P, it divides the circle into two equal semicircles. Therefore, angles RST and RTW are right angles.
Additionally, since RS is perpendicular to TW, angle STR is congruent to angle WTR by the definition of perpendicular lines.
Therefore, triangle RTW has two congruent angles (right angles) and one congruent side (RT) shared by both sides (RT and TW). Hence, triangle RTW is isosceles.