1. ESSENTIAL UNDERSTANDING: MATHEMATICAL PRACTICE:
Exploring Angle Pairs
BIG IDEA: REASONING AND PROOF
ESSENTIAL UNDERSTANDING:
Special angle pairs, such as adjacent, vertical, complementary, and supplementary angles, can be used to identify geometric relationships and to find angle measures
MATHEMATICAL PRACTICE:
Attend to precision

2. The five game pieces below form a square to fit back in the box
The five game pieces below form a square to fit back in the box. Two of the shapes are already in place. Where dot he remaining pieces go? How do you know? Make a sketch of the completed puzzle.
Getting Ready

3. Adjacent angles are ________ coplanar angles with a common __________, a common __________, and no common ____________ points.
Vertical angles are __________ angles whose sides are _______________ rays. The angles are _____________.
Linear pair is a __________ of ______________ angles whose noncommon sides are _______________ rays.
Linear Pair Postulate: If two angles
form a linear pair, then they are
_______________________
Types of Angle Pairs

4. Complementary angles are __________ angles whose measures have a sum of ________. Each angle is called the ______________ of the other.
Supplementary angles are __________ angles whose measures have a sum of __________. Each angle is called the _______________ of the other.
Types of Angle Pairs

5. Finding Information from a diagram
It is important in Geometry to understand the information a diagram can and cannot provide. It is tempting to make assumptions based on the appearance of a diagram, but assumptions must be limited either to special markings or to knowledge of special geometric relationships, such as special angle pairs.
You CAN conclude the following from an unmarked diagram: angles are adjacent; angles are adjacent and supplementary; and angles are vertical
You CANNOT conclude the following from an unmarked diagram: angles or segments are congruent; an angle is right; and angles are complementary
Finding Information from a diagram

6. EX 1: Identifying angles in the diagramb) c) d) e) f) g)
EX 1: Identifying angles in the diagram

7. 2. In one town, Main Street and Columbus Avenue intersect to form an angle of Find the measures of the other three angles.
3. a) Given that is a complement of , find
b) Given that is a supplement of , find
Examples

8. 4. Solve for x and y. Then find the angle measures.
Examples

9. Examples 5. are a linear pair, . What are the measures of each angle?
are complements and are supplements. If is four times , find the measure of each of the three angles.
Examples

10. 1.6 p – 36 evens, 46 – 52 evens, 53, 54, 66, 68, 72, 75
25 questions