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

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

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

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

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

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

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

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

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

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

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

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

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