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Various postulates and theorems related to proving that two lines are parallel in geometry. Topics include Postulates 10 and 11, Alternate Interior Angles Theorem, Same-Side Interior Angles Theorem, Perpendicular Lines, and various examples. Students of mathematics, particularly those studying geometry, will find this document useful for understanding the concepts of parallel lines and the different ways they can be proven.
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Comparing postulate 10 to postulate 11, what do you notice?
If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. We can rewrite postulates 10 and 11 into a single statement....
Notice that this is the converse of Theorem 3-2. We can rewrite them as the Alternate Interior Angle Theorem
Theorem 3-6 If two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel. Biconditional
Can we also write the Alternate Exterior Angle Theorem and Same-Side Exterior Angle Theorem as biconditionals? Theorem 3- In a plane two lines perpendicular to the same line are parallel. Remember Skew lines
Through a point outside a line, there is exactly one line perpendicular to the given line. Example 1: State which segments (if any) are parallel? State the postulate or theorem.
Example 2: Example 3: Find the value of x and y to make
