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Understanding Angles and Rays: Definitions, Notation, and Postulates

This instructional text covers the essential concepts of angles and rays in geometry. It defines angles as the intersection of two rays with a common endpoint, known as the vertex. It explains how to name angles using specific points and provides examples, including the Angle Addition Postulate. Additionally, the text discusses the concept of angle bisectors, which divide an angle into two congruent parts. It also includes a practical exercise for drawing diagrams, identifying angle measures, and applying the properties of angles and rays.

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Understanding Angles and Rays: Definitions, Notation, and Postulates

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Presentation Transcript

  1. Ch. 1.6 & 1.7 Angles

  2. RAYS • Have an end point and go on forever in one direction F H Name: starting point 1st, then another point 2nd Ex:

  3. Definition of an angle • two rays with a common endpoint, called the vertex ray vertex ray

  4. Angles and Points • Angles can have points in the interior, in the exterior or on the angle.

  5. Naming Angles • Three points on the angle • The vertex • A number

  6. Using three points • The vertex point MUST be the middle letter <CBA or <ABC

  7. Using Vertex • Must be the vertex of ONLY ONE angle • Ex: <B

  8. Using a number • A number written inside the angle close to the vertex AND the number is not the measurement • Ex: <2

  9. Angle Addition Postulate m<1 + m<2 = m<ADC • m<1 means the measure of <1 • m<1 + m<2=? m<ADC = 58.

  10. Angle Bisector • An interior ray of an angle splits the angle into two congruent angles • Since <4  <6, then is an angle bisector.

  11. Example • Draw your own diagram and answer this question: • If is an angle bisector of <PMY and m<PML = 87, then find: • m<PMY = _______ • m<LMY = _______

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