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MJ3 Ch 6.1 – Line & Angle Relationships 1. In art class Mark mixed 3 liters of yellow paint, 2 liters of red paint and 1 liter of blue paint. How many milliliters of paint did Mark mix in the bucket? 6 0 0 0 3 2 1 6 liters (1 liter = 1000 milliliters) 6 liters = 6000 milliliters • 0 1 2 3 4 5 6 7 8 9 / • 0 1 2 3 4 5 6 7 8 9 / • 0 1 2 3 4 5 6 7 8 9 / • 0 1 2 3 4 5 6 7 8 9 Bellwork – You do not have to write the question! • 0 1 2 3 4 5 6 7 8 9 Assignment Review None Before we begin…. Please take out your notebook and get ready to work… Today we will look at angles from a different perspective…That is angles formed by 2 parallel lines cut by a transversal…. Before we do that we need to make sure everyone understands the vocabulary used when talking about lines and angle relationships… Objective Students will identify line and angle relationships Vocabulary Acute Angles – have a measure less than 90° Right Angles – have a measure equal to 90° Obtuse Angles – have a measure greater than 90° Straight Angles – have a measure of 180° Vocabulary Parallel lines – Two lines on a plane that never intersect. Transversal – A line that intersects 2 parallel lines and creates 8 angles. Interior angles lie inside the parallel lines Exterior angles lie outside the parallel lines Alternate interior angles are on opposite sides of the transversal and inside the parallel lines Alternate exterior angles are on opposite sides of the transversal and outside the parallel lines. Corresponding angles are in the same position on the parallel lines in relation to the transversal Properties If two parallel lines are cut by a transversal, then the following pairs of angles are congruent. Corresponding angles are congruent Alternate interior angles are congruent Alternate exterior angles are congruent Let’s look at an example… Parallel Lines Cut by a Transversal a c e g a = 110° f h b d Your Turn In the notes section of your notebook draw two parallel lines cut by a transversal. Then find an acute angle and give it the measure of 60°. Then find the measure of the remaining angles. More Lines & Angle Relationships Intersecting Lines and Angles Vertical Angles – Angles formed by two intersecting lines. Vertical angles are congruent Example 4 1 3 2 Angles 1 & 3 are vertical angles Angles 2 & 4 are vertical angles Adjacent Angles When two angles have the same vertex, share a common side, and do not overlap they are adjacent angles Example Angle 1 & 2 are adjacent angles The mAOB = m1 + m2 A 1 2 O B Complimentary Angles If the sum of the measures of two angles equal 90°, the angles are complimentary Example: 3 4 1 2 You may see complimentary angles displayed 2 ways as pictured above. If the measures of the angles equal 90°, then they are complimentary Supplementary Angles If the sum of two angles equals 180°, then the angles are supplementary Example 1 2 3 4 You may see supplementary angles displayed 2 ways as pictured above. If the measures of the angles equal 180°, then they are supplementary Finding the Missing Measure You can find the missing measure of a pair of angles by classifying the angles then subtract the given measurement from the total measurement. Example: You can find the value of x by classifying the angles as supplementary and = 180° Then subtract 118° from 180° 118° to get the value of x = 62° x° Summary In the notes section of your notebook summarize the key concepts covered in today’s lesson Today we discussed… Parallel lines cut by a transversal Vertical angles Complimentary angles Supplementary angles Assignment Practice skills workbook Lesson 6.1 Reminder This assignment is due tomorrow. I do not accept late assignments