Angle Relationships and Special Angles on Parallel lines Objective: Students will be able to apply definitions of angles to determine missing angle measurements.
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)
Statement Reason <1+<2=180 Linear Pair <2+<3=180 <1+<2=<2+<3 Substitution <1=<3 Subtraction 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 Main properties with Parallel lines and Transversals Same side of transversal, nonadjacent, one interior and one exterior, congruent if lines are parallel Corresponding Angles Alternate Interior Angles Alternate Exterior Angles Same Side Interior Angles 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.
Objective: Students will be able to apply definitions of angles to determine missing angle measurements. On a scale of 1 to 4 Do you feel we meet the objective for the day. If we did not meet the objective, what did we miss and how could I improve.
Homework Pg 124 4,6,8 Pg 131 1-5 odd, 9 and 10 Honors pg 132 7