Answer:
To prove that triangle TUW is isosceles, we can use the fact that ray TV bisects angle ZUT and is an altitude in triangle TUW.
Since ray TV bisects angle ZUT, it splits the angle into two congruent angles, ZTV and TVU. This means that angle ZTV is congruent to angle TVU.
Since ray TV is an altitude in triangle TUW, it forms a right angle with the base of the triangle, which is line segment TU. This means that angle TVU is a right angle, and therefore, angle ZTV is a right angle as well.
Since angle ZTV and angle TVU are congruent right angles, we know that the two sides that form these angles, UT and TU, are congruent. This means that side UT is congruent to side TU, and therefore, triangle TUW is isosceles.