4.3,4.4,4.5 - Copy - 4-3 Some Remarks on Angles and 4-4...

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Unformatted text preview: 4-3 Some Remarks on Angles and 4-4 Perpendiculars, Right Angles and Related Angles, Congruent Angles A) Does the order of naming the angle matter? B) Order does matter in Trigonometry a. Directed Angles i. When we use directed angles, we allow "zero angles' and "straight angles" ii. We can think of directed angles as a rotation, we rotate the initial side until it falls on the terminal side 1. clockwise rotation - negative 2. counterclockwise rotations positive iii. Angles greater than 360. b. Radian measure i. Radians are used in directed angles more often than degrees ii. C = 2r and r = 1 Degrees Radians iii. So what is the radian measure for 1. 45 degree angle 2. 3. 90 degree angle 4. 5. 180 degree angle C) Types of Angles (all angles lie between 0 and 180) a. Acute angles i. Measure is less than 90 b. Right angles i. Measure is exactly 90 c. Obtuse angles i. Measure is greater than 90 d. Complementary angles i. Two angles whose sum in 90 1. they are called complements of each other e. congruent angles i. two angles with the same measure ii. A B and mA = mB mean exactly the same thing f. Perpendicular rays i. Two rays are perpendicular if they are the sides of a right angle two lines are perpendicular if they contain a pair of perpendicular rays symbol: 1. 2. g. Perpendicular i. Two sets are perpendicular if 1. each of them is a line, ray, or a segment, 2. they intersect, and 3. the lines containing them are perpendicular If AB AC , ii. then AB AC , AB AC , AB AC , and so on D) Equivalence relations a. Three properties i. Reflexive property 1. a = a for every a ii. Symmetric Property 1. If a = b, then b = a iii. Transitive Property 1. If a = b and b = c, then a = c b. The relation of congruence between angles has the same properties i. A A , for every A ii. If, A B , then B A iii. If A B and B C , then A C E) Theorem 4-1 a. Congruence between angles is an equivalence relation ...
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4.3,4.4,4.5 - Copy - 4-3 Some Remarks on Angles and 4-4...

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