Honors Geometry Section 1.3 part 1 Angles and Their Measures An *angle is the figure formed by the union of two rays with a common endpoint. The rays are called the sides ____ of the angle and their common endpoint is the vertex _____ of the angle. The same angle can be named in different ways: 1) by 3 points, with the middle point being the vertex ABC 2) by just the vertex – must have only one angle with this vertex 3) B The same angle can be named in different ways: 1) by 3 points, with the middle point being the vertex ABC 2) by just the vertex – must have only one angle with this vertex B 3) by using a number placed in the interior near the vertex 1 Angles are measured using a __________. protractor A common unit used for degree measuring angles is the ______. Radians and gradients are also used. mA We write ______to represent the measure of A . Postulate 1.3.2: Two angles are congruent iff their measures are equal. Tick marks are used to indicate congruent angles in a figure. mA We write ______to represent the measure of A . Postulate 1.3.2: Two angles are congruent iff their measures are equal. Tick marks are used to indicate congruent angles in a figure. Angles are classified according to their measure. An *acute angle is an angle whose measure is between 0 and 90 degrees. A *right angle is an angle whose measure is exactly 90 degrees. To indicate a right angle in a figure, place a small square at the vertex. Perpendicular lines are two lines that intersect to form right angles. To indicate that AB is perpendicular to CD , we write _________ AB CD An *obtuse angle is an angle whose measure is between 90 and 180 degrees. A *straight angle is an angle whose measure is exactly 180 degrees. 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 PQR , then m PQS m SQR m PQR An *angle bisector is the ray which divides an angle into two congruent angles. 2 x 8 2 x 8 96 8 x 16 4 x 80 8 x 16 E 2x 8 64 4 x x 16 m DBC 4 (16 ) 16 48 96 8 x 16