Question

1. sketch a line and a ray that intersect a plane at the same point

d. c is coplanar with plane liz.

Explanation:

Step1: Define the plane, line, and ray

Let's consider a plane, say plane \( P \). We'll define a point \( A \) on plane \( P \). Let the line be \( l \) and the ray be \( r \), both passing through point \( A \) and intersecting plane \( P \) at \( A \).

Step2: Sketching the plane

Draw a parallelogram (a common representation of a plane) to represent plane \( P \). Label the vertices if needed, but the key is to show a flat, two - dimensional surface.

Step3: Sketching the line and the ray

• For the line: Draw a straight line that passes through the plane \( P \) at point \( A \). The line should extend infinitely in both directions, with a portion inside and outside the plane (we can represent the part outside the plane with dashed lines if we want to show the hidden part, but for a basic sketch, a straight line through \( A \) in the plane and beyond is sufficient).
• For the ray: Draw a ray that starts at a point (let's say \( B \)) outside the plane \( P \) and passes through point \( A \) on the plane. The ray will have a starting point \( B \) and extend infinitely in the direction from \( B \) through \( A \), with \( A \) being the intersection point with the plane.

Answer:

To sketch a line and a ray that intersect a plane at the same point:

1. Draw a plane (e.g., a parallelogram) to represent the plane.
2. Mark a point \( A \) on the plane.
3. Draw a line passing through point \( A \) (the line extends infinitely in both directions, with part on either side of the plane).
4. Draw a ray with a starting point outside the plane that passes through point \( A \) (the ray starts at a point outside the plane and goes through \( A \), extending infinitely from the start point through \( A \)).

(Note: Since this is a sketching problem, the final answer is the described method of sketching. If a visual representation was required, it would be a diagram with a plane, a line through a point on the plane, and a ray through the same point on the plane.)