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Sections 3.2 and 3.3 Parallel Lines & Transversals Geometry Mr. Robinson Fall 2011

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Essential Question: What results can be determined when parallel lines are cut by a transversal?

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Postulate 15 Corresponding s Post. If 2 lines are cut by a transversal, then the pairs of corresponding s are . i.e. If l m, then 1 2. l m 1 2

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Section 3.2 Theorems Theorem 3.1 – If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.

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Section 3.2 Theorems Theorem 3.2 – If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.

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Section 3.2 Theorems Theorem 3.3 – If two lines are perpendicular, then they intersect to form four right angles.

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Theorem 3.4 Alternate Interior s Theorem If 2 lines are cut by a transversal, then the pairs of alternate interior s are . i.e. If l m, then 1 2. lmlm 1 2

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Theorem 3.5 Consecutive Interior s Theorem If 2 lines are cut by a transversal, then the pairs of consecutive int. s are supplementary. i.e. If l m, then 1 & 2 are supp. lmlm 1 2

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Theorem 3.6 Alternate Exterior s Theorem If 2 lines are cut by a transversal, then the pairs of alternate exterior s are . i.e. If l m, then 1 2. l m 1 2

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If a transversal is to one of 2 lines, then it is to the other. i.e. If l m, & t l, then t m. ** 1 & 2 added for proof purposes. 1 2 Theorem 3.7 Transversal Theorem lmlm t

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Ex: Find: m 1= m 2= m 3= m 4= m 5= m 6= x= 125 o 2 1 3 4 6 5 x+15 o

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Ex: Find: m 1=55 ° m 2=125 ° m 3=55 ° m 4=125 ° m 5=55 ° m 6=125 ° x=40 ° 125 o 2 1 3 4 6 5 x+15 o

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Assignment Pp. 138 – 139 #3-16 pp. 146 -147 #1-26

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1Geometry Lesson: Aim: How do we prove lines are parallel? Do Now: 1) Name 4 pairs of corresponding angles. 2) Name 2 pairs of alternate interior angles.

1Geometry Lesson: Aim: How do we prove lines are parallel? Do Now: 1) Name 4 pairs of corresponding angles. 2) Name 2 pairs of alternate interior angles.

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