Q28. - Geometry

Question

You can think of the ceiling and floor or a room as parts of horizontal planes. The walls are parts of vertical planes. Vertical planes are represented by figures like those shown in which two sides are vertical. A horizontal plane is represented by a figure like that shown, with two sides horizontal and no sides vertical.

a. Can two vertical planes intersect?

b. Suppose a line is known to be in a vertical plane. Does the line have to be a vertical line?

Step-by-Step Solution

Answer

1. Yes, the two vertical planes can intersect.
2. Suppose a line is known to be in a vertical plane. No, the line does not have to be vertical.

Part a. Step 1. Figures representing vertical planes.

The diagram of the vertical planes are

Part a. Step 2. Observe the diagram shown below.

Draw the two vertical planes as shown.

Part a. Step 3. Determine whether the vertical planes can intersect by considering the above figure.

From the above figure, it can be noticed that:

The two vertical planes $M$ and $N$ are intersecting on line $AB$. 

Therefore, yes, the two vertical planes can intersect.

Part b. Step 1. Figure representing vertical plane.

The diagram of the vertical plane is

Part b. Step 2. Observe the diagram shown below.

Construct one figure having a vertical line on the vertical plane and the other figure having a horizontal line on the vertical plane.

Part b. Step 3. Determine whether the line in a vertical plane is a vertical line by considering the above figure.

From the above figure, it can be noticed that:

The line in the vertical plane can be vertical as shown in the first figure, on the other hand, the line in the vertical plane can be horizontal as shown in the second figure.

Therefore, a line in the vertical plane does not have to be a vertical line.