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Geometry 1.6 ‐ Measuring Angles A. Angle (<) ‐ is formed by two rays that share a common endpoint • The rays are the sides of the endpoint • The endpoint is called the vertex of the angle • When naming an angle, we either name only the vertex, or name all three letters with the vertex named in the middle. EXAMPLE: Name the angle below in as many ways as possible. H D G • Congruent Angles ‐ two or more angles with the same measure In other words, if m<1 = m<2 then we say that <1 < 2 • We do not say that m<1 m<2. The “m” stands for the word “measure” and when we talk about the measure of an angle we are talking about its value. Values are equal, objects are congruent. Sep 92:59 PM 1 B. Classifying Angles. Write about the following types of angles and draw pictures of them on your notes. Acute angle ‐ • • Obtuse angle ‐ • Straight angle ‐ • Right angle ‐ Sep 93:38 PM 2 C. Angle Addition Postulate: Similar to the segment addition, if point B is in the interior of angle AOC then m<AOB + m<BOC = m<AOC. Furthermore, if <AOC is a straight angle, then m<AOB + m<BOC = 180 A B O B C A O C 1. Suppose m<1 = 42 and m<ABC = 88, use the angle addition postulate to find m<2. A 1 B 2 C Sep 93:40 PM 3 2. m<DAB = 740 A 3x 2x + 4 B D C Sep 1611:34 AM 4 D. Identifying Angle Pairs • Vertical Angles ‐ two angles whose sides are opposite rays 1 2 3 4 • Adjacent Angles ‐ to angles who share a common vertex and are beside each other 1 1 2 2 • Complementary Angles ‐ two angles whose measures have a sum of 90 350 2 1 550 • Supplementary Angles ‐ two angles whose measures have a sum of 180. 700 1100 1 2 Sep 93:45 PM 5 E. Examples. 1. Name all pairs of angles in the picture that are (a) Vertical 1 2 3 6 54 (b) Supplementary (c) Complementary (d) Adjacent Sep 93:47 PM 6 F. Drawing Conclusions: Listed below are things you can conclude from a diagram and things you cannot conclude Conclude: Adjacent angles • Adjacent supplementary angles • Vertical angles • Cannot Conclude: Angles or segments are congruent • An angle is a right angle • Lines are parallel or perpendicular • Sep 93:47 PM 7 Hon. Geom HW 1.6 p. 40 #s 1 8, 15 26, 35 37 Sep 1611:42 AM 8