Out of the alternate interior angles theorem, the corresponding angles theorem, and the alternate exterior angles theorem, which one is disproved by the parallel postulate?
Hint
They're all theorems, remember? Theorems.
Answer
None! The parallel postulate supports all three of these theorems. (Remember how theorems are statements of fact?)
Example 3
What are the values of m and n?
Hint
Corresponding angles are congruent. So are alternate interior angles.
Answer
m = 20, n = 27
Example 4
Are lines a and b parallel if p = 13 and q = 54?
Hint
Remember that vertical angles are congruent. What about consecutive interior angles?
Answer
No, lines a and b are not parallel.
Example 5
In what branch of geometry is the parallel postulate false?
Hint
Who came up with the parallel postulate? (His name rhymes with Shmooclid.)
