True or False:

If a ray bisects an angle of a triangle, then it also bisects the side opposite the angle.

If a plane intersects a cylinder, then the intersection must be a circle.

I think the first one is true and the second one is false.

both false

angle bisectors and medians are not the same lines.

To determine whether each statement is true or false, we can apply the definitions and properties of geometric figures.

1. If a ray bisects an angle of a triangle, then it also bisects the side opposite the angle.
This statement is false. A ray that bisects an angle of a triangle does not necessarily bisect the side opposite the angle. Consider an isosceles triangle, where the ray bisects the vertex angle. In this case, the ray only divides the side opposite the angle into unequal segments, resulting in a ratio other than 1:1.

2. If a plane intersects a cylinder, then the intersection must be a circle.
This statement is true. When a plane intersects a cylinder, the resulting intersection is indeed a circle. This is a property of cylindrical shapes, where any plane intersecting a cylinder perpendicular to its axis will create a circular cross-section.

So, your understanding is correct. The first statement is false, and the second statement is true.