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Geom A Unit 1 Day 5 1.4 and 1.5 Angles, Angle Pairs and Their Measures I. Angle - ______________________________________________________________________ _______________________________. The symbol for angle is . A. The endpoint of the rays is called the ___________________ of the angle. B. The size of the angle refers to the ___________________ between the rays, not the length of the sides of the angles. Name the bigger angle in each pair. 1 B 2 ________ is the bigger angle. A ________ is the bigger angle. C. When you name an angle, you sometimes can use a number included in the angle (like in the first eample) or one letter that is the vertex (like the second example), but sometimes, more detail is needed. Ex: If we were asked to give the measure for C in the diagram below, there could be some confusion. To clear things up, we’d use three letters, the middle one being the point where the angle bends. A B Give each of the following: 38 26 m ACB = _________ m BCD = _________ m ACD = _________ m BCA = _________ C D D. The example above shows us that PART + PART = WHOLE works for angles. II. Types of Angles and Measuring Angles A. Measures of angles in this course will be between 0 and 180 . B. A _________ angle measures 90 . C. An ________ angles measures less than 90 . D. An ________ angles measures more than 90 . E. A _____________ angle measure 180 . Label each diagram to the right with B, C, D or E to indicate the type of angle drawn. F. When you are measuring an angle using a protractor, it helps to know ahead of time whether the angle is ACUTE or OBTUSE. Tell whether the angle appears to be RIGHT, ACUTE or OBTUSE. Then record its measure. 1. 2. __________________ ________ ____________________ ________ 3. 4. ___________________ ________ ________________________ ________ III. Angle Addition Examples A. Remember that two types of angles have implied angle measures that might be needed to solve certain problems. 1. Right angles = 90 2. Straight angles = 180 H Q J a. b. c. G D 110 40 P L 60 45 E K N M F Find m DEF __________ Find m HJL __________ Find m QNM __________ B. A big angle made up of two or more parts can be the basis for an equation. a. POQ = (x 4) QOR = (2 x 2) POR = 26 1 x 24 2 LMP = x 136 PMN = 60 b. LMN = P O x = __________ m POQ = _________ Q P L M R x = __________ m LMN = _________ N II. Pairs of angles: A. Linear Pair - ___________________________________________________ ___________________________________________________ 1. Diagram of one linear pair Informal Observations: ____________ is your straight line. ______________ is an acute angle, it is right next to _________________, the obtuse angle, together they make a straight line. 2. Diagram of multiple linear pairs. A In the diagram to the right, there are 4 linear pairs of angles. One is given to you, the next is started for you. Complete that set and find the other two. AEC and CEB D E C are a linear pair AED and _________ are a linear pair ________ and _________ are a linear pair ________ and _________ are a linear pair III. Vertical Angles - ____________________________________________________ _____________________________________________________ _____________________________________________________ B 1. Example and Non-Example or Vertical Angles J A F C E H D G B K IV. Writing Equations Using Vertical Angles and Linear Pairs of Angles A. The measures of a linear pair ___________________________________ B. The measures of pair of vertical angles ______________________________ 1. Write an equation and solve for each variable. a) b) 6 y 80 E 2 y D 72 A 3x E y = _____________ a 60 4b H H B 2 J F C x = ___________ c.) 1 G G J 132 a = ________ b = ________ F V. Two Pairs of Angles that Don’t Rely on a Diagram A. Complementary – Any two angles that _____________________________ B. Supplementary – Any two angles that _____________________________ Ex: Find the complement of a 49 angle. ____________ Ex: If A is 4 times larger than B, find the measures of both angles, given that they are supplementary to each other. HW: Geometry A Unit 1 Day 5 HW