Special Angles on Parallel lines Some angle relationships revisited

Linear Pair – adjacent angles that are supplementary Adjacent angles – two angles that have the same vertex and share a side Vertical Angles – angles formed by intersecting lines, opposite each other, share vertex but no sides, they are congruent

Given the picture prove why angle 1 and 3 are congruent without using vertical angles. (deductive reasoning)

StatementReason <1+<2=180Linear Pair <2+<3=180Linear Pair <1+<2=<2+<3Substitution <1=<3Subtraction Angle 1 and 2 are a linear as are 2 and 3. Since both are linear pairs both equal 180 therefore are equal to each other. Angle 2 is common in both and can be removed therefore angle 1 is equal to angle 3

Relationships of Lines Parallel lines – lines that never touch, have same slope symbol = || Perpendicular lines – lines that intersect and form right angles, slopes are opposite reciprocals symbol =

Parallel Lines and a Transversal Transversal – line that intersects two or more lines at different points There are relationships between some of the angles, if the lines the transversal crosses are parallel then there are more properties Need to state lines are parallel do not assume that they are, symbol for parallel lines both have an arrow on line.

Interior Angles – angles that are between the two lines that the transversal crosses Exterior Angles – angles outside the two lines that the transversal crosses

4 Maim properties with Parallel lines and Transversals Corresponding Angles Alternate Interior Angles Alternate Exterior Angles Same Side Interior Angles Same side of transversal, nonadjacent, one interior and one exterior, congruent if lines are parallel Both interior angles, opposite sides of transversal, nonadjacent, congruent in lines are parallel Both exterior, opposite sides of the transversal, nonadjacent, congruent if lines are parallel Both Interior, same side of the transversal, supplementary if lines are parallel

Backward Properties Know that the reverse of the properties can be true. If corresponding angles are congruent then the lines are parallel. If alternate interior angles are congruent then the lines are parallel.

Homework Pg 124 4,6,8 Pg odd, 9 and 10 Honors pg 132 7