What does the intersection of two planes look like?

Conditions

• Two distinct planes are given.
• The planes are not parallel or skew; they intersect.

Reasoning, step by step

1. Visualize two flat surfaces crossing each other.
2. Identify the set of points common to both planes.
3. Recognize that this common set of points forms a straight line.
4. Name the line using a lowercase letter (e.g., line m) or two points on it (e.g., $\overleftrightarrow{XW}$).

Example

The instructor shows two intersecting planes and states: 'if planes intersect they're gonna cross at a line.' He names the intersection line m or $\overleftrightarrow{XW}$.

Common misconceptions

• Thinking two planes intersect at a point.
• Confusing the intersection of lines (a point) with the intersection of planes (a line).

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Explore next

• How do you name a ray?
• What is the intersection of line l and line m?