2/7/2018. Check HW. Objectives: How many angles are there? Table of Contents (2 nd Semester) 40 o 1 2. Angles formed by Parallel Lines
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1 /7/08 Created by Stephen Ackerman Warmup / tan π 4 7. Find the measures of all marked angles in the diagram. Created by Stephen Ackerman Warmup / tan π 7 4. Find the measures of all marked angles in the diagram. 40 o 0 o 3 7 o 4 m = m = m 3 = m 4 = m = 40 o 0 o 3 7 o 4 m = 60 o m = 80 o m 3 = 60 o m 4 = 0 o m = 4 o Check HW Table of Contents ( nd Semester) p. Exponent Basics (.) p. Multiplying and Dividing Powers (.3) p. 3 Power to a Power (.4) p. 4 Zero & Negative Exponents (.) p. Scientific Notation (.6) p. 6 Calcluating with Scientific Notation (.7) p. 7 Angle Basics p. 8 Angles formed by Parallel Lines (.) Angles formed by Parallel Lines Objectives: Given one angle measure, find ALL angles formed by parallel lines Identify special angle pairs Use special angle pair rules to find angle measures 7 How many angles are there? l m n
2 /7/08 DISCUSS WITH YOUR GROUP: The red arrows mean that lines m and n are parallel. In your group, take turns discussing which PAIRS of angles you think are congruent. (For example: I think that angles and 3 are congruent because ) I will randomly pick a representative from a few groups to share what your group discussed: Which angles did you think were congruent? Why do you think they are l congruent? Did your group all agree or not? m n COPY the diagram!!!! Two angles that are in the same position but on different lines are called corresponding. One angle measure is given. Find the measures of ALL other angles. If the lines are parallel, these angles will be congruent!!! o m = 4 o m = 3 o m 3 = 4 o m 4 = 4 o m = 3 o m 6 = 3 o m 7 = 4 o One angle measure is given. On your whiteboard, find the measures of ALL other angles. m = 8 o m = 98 o m 3 = 8 o m 4 = o 7 o m = 98 o m 6 = 8 o m 7 = 8 o New terminology Which angles would you say are interior angles? Which angles would you say are exterior angles?
3 /7/08 New terminology : between the parallel lines Exterior: outside the parallel lines : opposite sides of the transversal Same-side: same side of the transversal Copy into binder: : 4 and, 3 and 6 Same-side : 3 and, 4 and 6 Exterior: and 8, and 7 Give me an example of: A pair of alternate interior angles A pair of same-side interior angles A pair of alternate exterior angles : and, and 6, 3 and 7, 4 and 8 Exterior Same-side Vertical 3
4 /7/08 Same-side interior Vertical Supplementary 4
5 /7/08 Same-side interior What is ALWAYS true about alternate interior angles? What is ALWAYS true about same-side interior angles?
6 /7/08 IN YOUR BINDER What is ALWAYS true about alternate exterior angles? ONLY WHEN THE LINES ARE PARALLEL: : congruent Exterior: congruent Same-side : supplementary If the measure of angle is 30 degrees, what is the measure of angle? HOW DO YOU KNOW? If the measure of angle is 4 degrees, what is the measure of angle? HOW DO YOU KNOW? m = 30 o ; they are alternate exterior m = 3 o ; they are same-side interior If the measure of angle is degrees, what is the measure of angle? HOW DO YOU KNOW? m = o ; they are vertical If the measure of angle is degrees, what is the measure of angle? HOW DO YOU KNOW? m = o ; they are corresponding 6
7 /7/08 If the measure of angle is 07 degrees, what is the measure of angle? HOW DO YOU KNOW? m = 07 o ; they are alternate interior If the measure of angle is 4 degrees, what is the measure of angle? HOW DO YOU KNOW? m = 39 o ; they are supplementary If the measure of angle is 4 degrees, what is the measure of angle? HOW DO YOU KNOW? Extra one If the measure of angle is 40 degrees, what is the measure of angle? HOW DO YOU KNOW? TRICK QUESTION: These lines aren t parallel. We don t know! 3 m = 40 o ; angle 3 is 40 degrees because it corresponds to angle ; angle is supplementary with angle 3 HOMEWORK p.37 ( 8, 0) 7
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