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Understanding Angles: Definitions, Measurements, and Classifications in Geometry

This section discusses the fundamental concept of angles in geometry, defining an angle as the figure formed by two rays sharing a common endpoint. It covers terminology including sides and vertex, the various ways to name angles, and the measurement of angles using tools like protractors, with degrees as the primary unit. Additionally, it categorizes angles as acute, right, obtuse, and straight, explaining their respective measures, and introduces the Angle Addition Postulate and angle bisectors, crucial for understanding angle relationships.

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Understanding Angles: Definitions, Measurements, and Classifications in Geometry

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  1. Geometry Section 1.4Angles and Their Measures

  2. An *angle is the figure formed by the union of two rays with a common endpoint.The rays are called the ____ of the angle and their common endpoint is the _____ of the angle. sides vertex

  3. The same angle can be named in different ways:1) 2) 3) by 3 points, with the middle point being the vertex by just the vertex – must have only one angle with this vertex

  4. The same angle can be named in different ways:1) 2) 3) by 3 points, with the middle point being the vertex by just the vertex – must have only one angle with this vertex by using a number placed in the interior near the vertex

  5. Angles are measured using a __________.A common unit used for measuring angles is the ______. Radians and gradients are also used. protractor degree

  6. We write ______to represent the measure of .Postulate 1.3.2: Two angles are congruent iffTick marks are used to indicate congruent angles in a figure. their measures are equal.

  7. We write ______to represent the measure of .Postulate 1.3.2: Two angles are congruent iffTick marks are used to indicate congruent angles in a figure. their measures are equal.

  8. Angles are classified according to their measure.An *acute angle is an angle whose measure is A *right angle is an angle whose measure is between 0 and 90 degrees. exactly 90 degrees.

  9. To indicate a right angle in a figure, place a small square at the vertex.Perpendicular lines are two lines that intersect To indicate that is perpendicular to , we write _________ to form right angles.

  10. An *obtuse angle is an angle whose measure is A *straight angle is an angle whose measure is between 90 and 180 degrees. exactly 180 degrees.

  11. The Angle Addition Postulate is similar to the Segment Addition Postulate.Postulate 1.3.3: Angle Addition Postulate: If S is in the interior of , then

  12. An *angle bisector is the ray which divides an angle into two congruent angles.

  13. E

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