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Geometry

This comprehensive guide explores the fundamental concepts of angles, including their definitions, measurement techniques, and classifications. Discover how to name angles and utilize a protractor to measure them in degrees. Learn about congruent angles, the distinction between interior and exterior points related to angles, and the Angle Addition Postulate. We also examine specific scenarios like overlapping angles, and guide you step-by-step to classify angles as acute, right, obtuse, or straight using geometric principles.

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Geometry

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  1. Geometry 1.4 Angles and Their Measure

  2. Angles An angleconsists of two different rays that have the same initial point. The rays are the sides of the angle. The initial point is the vertex of the angle.

  3. Naming Angles • Name the angles in the figure

  4. The measure of an angle can be approximated with a protractor, using units called degrees.Let’s try measuring some….

  5. Congruent Angles Angles that have the same measure are called congruent angles.

  6. Interior vs Exterior A point is in the interior of an angle if it is between points that lie on each side of the angle A point is in the exterior of an angle if it is not on the angle or in its interior.

  7. Name the Interior and Exterior Points

  8. Angle Addition Postulate If B is in the interior of AOC, then Thus, the measure of the bigger angle is the sum of the measure of the two smaller ones

  9. A lawn is watered by a sprinkler that has two fixed spray heads that each spray water in a fan shape. The angle that determines each of the fan shapes is 120. The shaded area in the diagram shows where the two fan shapes overlap. Find the measure of angle 2 30 30 1 2 3

  10. Classifying Angles

  11. Plot the following Points • L(-5, 3) • M(-1, -1) • N(3, 3) • Q(5, -1) • P(3, -5)

  12. Measure and classify the following angles as acute, right, obtuse, or straight • Angle LMN • Angle LMP • Angle NMQ • Angle LMQ

  13. Two angles are adjacent angles if they share a common vertex and side, but have no common interior points

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