3-3+Parallel+Lines

3-3 Parallel Lines-

http://regentsprep.org/Regents/math/geometry/GP8/Lparallel.htm http://www.mathnstuff.com/math/spoken/here/2class/260/trans.htm

A transversal is a line that intersects one or more lines in a plane. Parallel Lines are two or more lines that will never intersect. When cut by a transversal, they form angles. Then there are theorems and postulates we can use to solve them. This section teaches us how to use different postulates and theorems to determine if the angles are congruent or not. Some of the theorems that are in this section are the Corresponding Angles Postulate, Alternate Interior Angles Postulate, Consecutive Interior Angles Theorem, Alternate Exterior Angles Theorem, and Perpendicular Transversal Theorem. (Chapter 3 Section 3)


 * Corresponding Angles Postulate**- If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
 * Alternate Interior Angles Theorem**- If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
 * Consecutive Interior Angles Theorem**- If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are congruent.
 * Alternate Exterior Angles Theorem**- If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.
 * Perpendicular Transversal Theorem**- If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to each other.

This is one example of parallel lines cut by a transversal. X would also equal 127 degrees because of the Corresponding Angles Postulate.

Angles 4 and 3 are congruent because of Alternate Interior Angles Theorem.

Angles H and K are congruent due to Alternate Exterior Angles Theorem.

Practice Questions Name the relationship if any. (answers at bottom of page)

What is the relationship between angles 3 and 6?

What is the relationship between angles 1 and 7?

What is the relationship between angles 2 and 7?

What is the relationship between angles 6 and 8?

Answers 1. Alternate Interior Angles Theorem 2. No relationship 3. Alternate Exterior Angles Theoem 4. Corresponding Angles Postulate