There is a similar postulate about the intersection of planes.
Take note Postulate 1-3
If two distinct planes intersect, then they intersect in exactly one line.
Plane RST and plane WST intersect in
When you know two points that two planes have in common, Postulates 1-1 and 1-3 tell you that the line through those points is the intersection of the planes.
Problem 3 Finding the Intersection of Two Planes
Each surface of the box below represents part of a plane. What is the intersection of plane ADC and plane BFG?
| Know | Need | Plan |
|---|---|---|
| Plane ADC and plane BFG | The intersection of the two planes | Find the points that the planes have in common. |
Think
Is the intersection a segment?
No. The intersection of the sides of the box is a segment, but planes continue without end. The intersection is a line.
|
Focus on plane ADC and plane BFG to see where they intersect. |
|
You can see that both planes contain point B and point C. |
The planes intersect in
✓ Got It?
-
- What are the names of two planes that intersect in
- Reasoning Why do you only need to find two common points to name the intersection of two distinct planes?
- What are the names of two planes that intersect in
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs