Q3. - Geometry

Question

Planes $\mathbf{M}$ and $\mathbf{N}$ are known to intersect.

1. What kind of figure is the intersection of $\mathbf{M}$ and $\mathbf{N}$?
2. State the postulate that supports your answer to part (a).

Step-by-Step Solution

Answer

1. The kind of figure that is formed by the intersection of the planes $M$ and $N$ is a line.
2. The postulate that supports the answer to part (a) is postulate 9 which states that if the two planes intersect then the intersection of these two planes is a line.

Part a. Step 1. Draw the planes M and N such that they are intersecting.

The diagram showing the planes $M$ and $N$ which are intersecting is:

Part a. Step 2. Observe the diagram.

It can be noticed from the diagram that the planes $M$ and $N$ are intersecting each other and the intersection of the plane is a line $AB$.

Part a. Step 3. Name the figure that is formed by the intersection of the planes M and N.

Therefore, it can be noticed that the figure is formed by the intersection of the planes $M$ and $N$ is a line.

Part b. Step 1. Write the answer to part (a).

The figure is formed by the intersection of the planes $M$ and $N$ is a line.

Part b. Step 2. Write the postulate 9.

If the two planes intersect then the intersection of these two planes is a line.

Part b. Step 3. Name the postulate that supports the answer to part (a).

It can be noticed that:

Postulate 9 states that if the two planes intersect then the intersection of these two planes is a line that supports the answer to part (a).