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Understanding Angles and Rays in Geometry

Learn the basics of angles, rays, and angle bisectors in geometry, including definitions, naming conventions, and the angle addition postulate. Explore examples to deepen your understanding.

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Understanding Angles and Rays in Geometry

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  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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