In the following figure, determine the intersection of plane 𝐴𝐷𝐴 prime and plane 𝐵𝐷𝐵 prime.
First, let’s identify plane 𝐴𝐷𝐴 prime. 𝐴𝐷𝐴 prime, we know that a plane is a flat two-dimensional surface that extends infinitely. And that means that plane 𝐴𝐷𝐴 prime does not just include this triangular piece. It includes these spaces and continues to extend in all directions.
Let’s go ahead and identify the plane space that includes 𝐵𝐷𝐵 prime. 𝐵𝐷𝐵 prime, here is the shape created by 𝐵𝐷𝐵 prime. And here is a representation of the plane that 𝐵𝐷𝐵 prime lies in. Here’s a reduced sketch of these two planes.
We remember that the intersection of two planes is a line. We need to identify the line that is the intersection of these two planes. Line 𝐶𝐶 prime is the intersection of these two planes. What we mean by that is at every point along the line 𝐶𝐶 prime is both plane 𝐴𝐷𝐴 prime and plane 𝐵𝐷𝐵 prime.