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

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

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

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

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

EX 1: Identifying angles in the diagram b) c) d) e) f) g) EX 1: Identifying angles in the diagram

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

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

Examples 5. are a linear pair, . What are the measures of each angle? 6. are complements and are supplements. If is four times , find the measure of each of the three angles. Examples

1.6 p. 47 8 – 36 evens, 46 – 52 evens, 53, 54, 66, 68, 72, 75 25 questions