- Define complementary angles, supplementary angles, adjacent angles, linear pairs, and vertical angles.
- Use angle pair relationships to write and solve equations
- Apply the Linear Pair Postulate and the Vertical Angles Theorem.
- The measures of complementary angles add up to ___________.
The two angles below are complementary. What is the measure of each angle?
If the angles are complementary, then their measures add up to __________.
1. When angles are complementary, what does their sum equal?
- The measures of supplementary angles add up to ________________.
If the angles are supplementary, then their measures add up to ____________.
- ____________________________ angles are next to each other: they share the same vertex and one side.
Adjacent is a word meaning “next to.”
Things that are adjacent are usually touching, and they share a border.
Oregon, Nevada, and Arizona are adjacent to California because they share a border with California.
Now we are ready to talk about linear pairs. A linear pair is two angles that are adjacent and whose non-common sides form a straight line.
Linear pairs are angles that are next to each other along a _________________ line.
Linear pairs are so important in geometry that they have their own postulate.
Linear Pair Postulate
If two angles are a linear pair, then they are supplementary.
The two angles below form a linear pair. What is the value of each angle?
1. Fill in the blank:
Now that you understand supplementary and complementary angles, you can examine more complicated situations.
Special angle relationships are formed when two lines intersect, and you can use your knowledge of linear pairs of angles to explore each angle further.
Vertical angles are non-______________________________, which means they are not next to each other.
Vertical angles are formed by _______________________________ lines, and as you can see in the diagram below, they are always directly across from each other at the intersection:
Vertical Angles Theorem
The Vertical Angles Theorem states that if two angles are vertical angles then they are congruent.
Vertical angles are _____________________________ to each other.
Introduction to Proof: Proving the Vertical Angle Theorem
Here is proof that vertical angles will always be congruent:
1. Fill in the blank: The reason that vertical angles are congruent is that each pair of adjacent angles is a ___________________________ pair.
Graphic Organizer for Lesson 8