Angles and Their Measures 1 4 Angles and
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Angles and Their Measures
1. 4 Angles and Their Measures GOAL 1 Use Angle Postulates GOAL 2 Classify angles as acute, right, obtuse, or straight.
1. 4 GOAL Angles and Their Measures 1 USING ANGLE POSTULATES Naming Angles An _____ angle consists of two different rays that have the same initial point. The rays are the _____ sides of the angle and the initial point is the ______. vertex C Vertex A e Side B
C Naming Angles A The three names for this angle: The middle point is the vertex B
Naming Angles How many angles do you see? THREE
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 mean any of the angles. could
Measuring Angles The expression is read as “the ____ measure of angle A. ” 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 and The units used to measure angles are called _______, the symbol for them is a _.
Measuring With a Protractor Read OUTTER scale from LEFT to RIGHT 55º One side of the angle lined up along the LEFT half of the protractor Vertex
Measuring With a Protractor Read INNER scale from RIGHT to LEFT 145º Vertex One side of the angle lined up along the RIGHT half of the protractor
Let’s measure some angles. R M Y T Q S
Measuring Angles Let’s measure some angles. R Y Q Since congruent _____. M T S we say that the angles are Remember: Angles are congruent, measures are equal. Incorrect: Correct: and
Constructing Angles http: //www. mathsisfun. com/geometry/protract or-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 ____ measure of EXAMPLE Find Use either scale on the protractor to find it, but use the same one for both rays. Solutions: A B or O
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 _______ interior of the angle. A point that is not on an angle or in its interior is in the ____ exterior of the angle. A interior exterior B 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 P S T
Checkpoint D 1. Name the angles in the figure. C E 2. In the figure above, Find the measure of Solution: and. F
1. 4 GOAL Angles and Their Measures 2 CLASSIFYING ANGLES Right Acute Obtuse Straight
Angles are classified according to their angle measure Classification Example ACUTE Measure 0º < < 90º A RIGHT = 90º A OBTUSE STRAIGHT A A 90º < < 180º = 180º
Two angles that share a common vertex and side, but have no common interior points, are called ____ adjacent angles. D A C Name the two adjacent angles in the diagram. B The common vertex is __ D and the common side is ___.
Example Use a protractor to draw two adjacent angles and so that is acute and is straight. N L Classify M O as acute, right, obtuse, or straight: obtuse
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