3.3 Parallel Lines and Transversals Proving angles congruent with parallel lines.

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Presentation transcript:

3.3 Parallel Lines and Transversals Proving angles congruent with parallel lines

Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent

Alternate Interior Angles If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent

Alternate Exterior Angles If two parallel lines are cut by a transversal, then the pairs of alternate exterior interior angles are congruent

Consecutive Interior Angles If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary

Perpendicular Transversal If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line. If k // l and k m, kl then l m m

Given: p // q Prove: #1. p // q #1.Given

Given: p // q Prove: #1. p // q #1.Given 3 1 #2.#

Given: p // q Prove: #1. p // q #1.Given 3 1 #2.#2.Linear pairs 5 6 are Supplementary

Given: p // q Prove: #1. p // q #1.Given 3 1 #2.#2.Linear pairs 5 6 are Supplementary 7 8 #3. 4 2

Given: p // q Prove: #1. p // q #1.Given 3 1 #2.#2.Linear pairs 5 6 are Supplementary 7 8 #3.#3.If two parallel lines 4 2 are cut by a transversal, then Corr. Angles are congruent.

Given: p // q Prove: #1. p // q #1.Given 3 1 #2.#2.Linear pairs 5 6 are Supplementary 7 8 #3.#3.If two parallel lines 4 2 are cut by a transversal, then Corr. Angles are congruent. #4.

Given: p // q Prove: #1. p // q #1.Given 3 1 #2.#2.Linear pairs 5 6 are Supplementary 7 8 #3.#3.If two parallel lines 4 2 are cut by a transversal, then Corr. Angles are congruent. #4.#4.Def. of congruent

Given: p // q Prove: #1. p // q #1.Given 3 1 #2.#2.Linear pairs 5 6 are Supplementary 7 8 #3.#3.If two parallel lines 4 2 are cut by a transversal, then Corr. Angles are congruent. #4.#4.Def. of congruent #5.

Given: p // q Prove: #1. p // q #1.Given 3 1 #2.#2.Linear pairs 5 6 are Supplementary 7 8 #3.#3.If two parallel lines 4 2 are cut by a transversal, then Corr. Angles are congruent. #4.#4.Def. of congruent #5.#5.Substitution

Solve for x 1

X

Homework Page #8 – 10, odd, #8 – 10, odd, 29, 31 29, 31

Homework Page #12 – 28 even,