MJ2A Ch 10.1 – Line & Angle Relationships

Bellwork Draw the triangle, find the value of x, then classify the triangle as acute, obtuse or right. x°x°68° 57° 1. 28° 62°x°x° 2. 32° 36°x°x°

Assignment Review Your Classifying Triangle Poster is due today. Make sure that your name is on the BACK, then pass it forward

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 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 = 110° ab cd ef g h

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 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 1 2 Angle 1 & 2 are adjacent angles The m  AOB = m  1 + m  2 A O B

Complimentary Angles If the sum of the measures of two angles equal 90°, the angles are complimentary Example: 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 You may see supplementary angles displayed 2 ways as pictured above. If the measures of the angles equal 180°, then they are supplementary

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 section 10.1 Reminder  This assignment is due tomorrow.