Angles and Their Measures

1.4 Angles and Their Measures 1 2 GOAL Use Angle Postulates GOAL Classify angles as acute, right, obtuse, or straight.

1 1.4 Angles and Their Measures GOAL USING ANGLE POSTULATES Naming Angles An _____ consists of two different rays that have the same initial point. angle The rays are the _____ of the angle and the initial point is the ______. sides vertex A C B Vertex Side Side

Naming Angles A C B The three names for this angle: The middle point is the vertex

How many angles do you see? Naming Angles How many angles do you see? THREE

Name the angles in the figure. EXAMPLE Name the angles in the figure. Answers: 1. 2. 3. Why should you not use to name any angle in the figure? All three angles have N as the vertex, so could mean any of the angles.

Measuring Angles The expression is read as “the ________ of angle A.” measure IMPORTANT!!! Note the difference in notation between an angle and its measure. Always use the correct notation!!! The tool used to measure angles is called a _________. protractor degrees The units used to measure angles are called _______, and the symbol for them is a _.

55º Measuring With a Protractor Read OUTTER scale from LEFT to RIGHT Vertex One side of the angle lined up along the LEFT half of the protractor

145º Measuring With a Protractor Read INNER scale from RIGHT to LEFT One side of the angle lined up along the RIGHT half of the protractor Vertex

Let’s measure some angles. Y R M Q T S

Measuring Angles Q R S Let’s measure some angles. Y M T Since we say that the angles are _________. congruent Remember: Angles are congruent, measures are equal. Incorrect: Correct: and

Constructing Angles http://www.mathsisfun.com/geometry/protractor-using.html

PROTRACTOR POSTULATE For any point A on one side of , can be matched one to one with the real numbers from 0 to 180. The absolute value of the difference between the real numbers for is the ________ of measure Find Use either scale on the protractor to find it, but use the same one for both rays. EXAMPLE A B O Solutions: or

To understand the next postulate, you must understand some vocabulary: A point that is between points that lie on each side of an angle is in the _______ of the angle. A point that is not on an angle or in its interior is in the ________ of the angle. interior exterior exterior B interior A Z In the above diagram, A is in the interior of the angle and B is in the exterior of the angle.

ANGLE ADDITION POSTULATE If P is in the interior of then R T P S

Checkpoint D Name the angles in the figure. C F E In the figure above, and Find the measure of . Solution:

1.4 Angles and Their Measures 2 Right Acute Obtuse Straight GOAL CLASSIFYING ANGLES Right Acute Obtuse Straight

Angles are classified according to their angle measure Classification Example Measure ACUTE 0º < < 90º RIGHT = 90º OBTUSE 90º < < 180º STRAIGHT = 180º A A A A

The common vertex is __ and the common side is ___. Two angles that share a common vertex and side, but have no common interior points, are called ________ angles. adjacent A B C D Name the two adjacent angles in the diagram. The common vertex is __ and the common side is ___. D

Example Use a protractor to draw two adjacent angles and so that is acute and is straight. L N M O Classify as acute, right, obtuse, or straight: obtuse