Question

If two planes intersect, then they intersect in exactly one line. Planes R and S intersect. Use deductive reasoning to write a conclusion.

Answer 1

If two planes intersect, they intersect in exactly one line.

Step-by-step explanation:

Premise 1: Planes R and S intersect.

Premise 2: Two planes can only intersect in two ways: either they intersect in exactly one line or they intersect in infinitely many lines.

Conclusion: Planes R and S intersect in exactly one line.

Step-by-step explanation:

Premise 1 states that Planes R and S intersect. Premise 2 states that there are only two possible ways for two planes to intersect. Since Premise 1 eliminates one of those possibilities (that Planes R and S intersect in infinitely many lines), the only remaining possibility is that Planes R and S intersect in exactly one line.

Therefore, we can conclude that Planes R and S intersect in exactly one line.

Answer 2

Planes R and S intersect in exactly one line.