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Understanding Angles: Types, Bisectors, and the Angle Addition Postulate

This educational resource explores the fundamentals of angles, including the Angle Addition Postulate and the concepts of congruent angles and angle bisectors. You'll learn how to measure angles formed by two rays with a common endpoint, identify types of angles (acute, right, obtuse), and understand interior and exterior regions created by an angle. With examples and clear definitions, this guide is designed to enhance your geometric knowledge and help you apply these concepts in mathematical problems involving angles.

andrew-livingston
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Understanding Angles: Types, Bisectors, and the Angle Addition Postulate

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Presentation Transcript

  1. 1-6 Exploring Angles OBJECTIVES: Use the Angle Addition Postulate to find the measures of angles Use congruent angles and the bisector of an angle

  2. Ray • Extends indefinitely in one direction. • EXAMPLES: • The endpoint must be the first letter in the name . R . . . H M D Ray MR (MR) Ray DH ( DH)

  3. Opposite Rays • Form a line • Referred to as a straight angle • CB and CM are opposite rays . . . B C M

  4. Angle • Formed by two rays with a common starting point. • The two rays are called the sides • The common endpoint is the vertex • EXAMPLE: <ABC <B <1 . A . . B 1 C

  5. Types of Angles • Acute Angles – measure less than 90º • Right Angles – measure 90º • Obtuse Angles – measure more than 90º

  6. Interior and Exterior of Angles An angle separates a plane into three distinct parts: • Interior • Exterior • Angle itself Interior Exterior

  7. Angle Bisector • A ray that divides an angle into two congruent angles

  8. Congruent Angles • Angles that have the same measure

  9. Angle Addition Postulate • If R is in the interior of PQS, then mPQR + mRQS = mPQS. P R Q S

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