https://file.aiquickdraw.com/mathbot/file/1726329022755ypia0lum.jpg

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.

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### 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.

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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.

Determine if each of the following statements are true or false. If false, explain why.

(a) Two intersecting lines are coplanar.
(b) Three noncollinear points are always coplanar.
(c) Two planes can intersect in exactly one point.
(d) A line segment contains an infinite number of points.
(e) The union of two rays is always a line.

Explore key geometric concepts such as coplanarity, line intersections, and the properties of rays and line segments. This problem helps students in grades 9-11 understand the relationships between planes, lines, and points.

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