Let's go through each statement and question from the image and explain the correct answers.

Part 1: True/False Statements

a. Two intersecting lines are coplanar.

• True. Two lines that intersect must lie in the same plane because they share a common point. Hence, they are coplanar.

b. Three noncollinear points are always coplanar.

• True. Any three points, as long as they are not collinear, define a unique plane. This is a geometric principle.

c. Two planes can intersect in exactly one point.

• False. When two planes intersect, they typically do so along a line, not at a single point. A plane would intersect at a point only in degenerate cases, like when two planes are tangent at a point, but that isn't typical.

d. A line segment contains an infinite number of points.

• True. A line segment, though finite in length, contains infinitely many points.

e. The union of two rays is always a line.

• False. The union of two rays is a line only if they are opposite rays (i.e., they have the same starting point and extend in opposite directions). Otherwise, the union of two rays is not necessarily a line.

Part 2: Multiple Choice

a. Choose the correct answer:

• The correct choice is A: The statement is true.
  • Two intersecting lines are always coplanar because they meet at a point and must lie in the same plane.

b. Choose the correct answer:

• The correct choice is B: The statement is true.
  • Three noncollinear points are always coplanar as they define a unique plane.

Do you want further details or have any specific questions?

Here are 5 related questions to deepen your understanding:

1. Can two non-intersecting lines in 3D space be coplanar?
2. How many points are needed to uniquely define a plane?
3. What is the geometric condition for two planes to intersect along a line?
4. Can a single point determine if two lines are coplanar or skew?
5. What is the difference between opposite rays and any two rays?

Tip: To understand geometric relationships, visualize them in 2D and 3D space; this can help clarify concepts like coplanarity and intersections.