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Intro Chapter 1.4 Angles.notebook September 16, 2014 1.4 Measuring Angles Objective: To find the measures of angles M.2.B. Performance Standard 1.6, 3.4, 3.5 DOK1, 2 Knowledge MA 3 What is an angle??? Angle Formed by two rays with the same endpoint. Vertex the endpoint of an angle Sides Each ray of the angle E How do you NAME angles??? A Name the following angles: 2 B 1 D C F How do you CLASSIFY angles??? Acute angle An angle that measures between 0 and 90 degrees. Right angle An angle that measures 90 degrees. Obtuse angle An angle that measures between 90 and 180 degrees. Straight angle An angle that measures 180 degrees. 1 Intro Chapter 1.4 Angles.notebook September 16, 2014 2 Intro Chapter 1.4 Angles.notebook September 16, 2014 3 Intro Chapter 1.4 Angles.notebook September 16, 2014 4 Intro Chapter 1.4 Angles.notebook September 16, 2014 Postulate 1.7 Protactor Postulate (similar to ruler postulate) We can measure angles in terms of real numbers from 0 to 180 degrees. How do you measure angles??? Practice with handout. 5 Intro Chapter 1.4 Angles.notebook September 16, 2014 6 Intro Chapter 1.4 Angles.notebook September 16, 2014 Postulate 18: Angle Addition Postulate Adjacent angle measures can be added together to form a large angle measure. C A m < ABC + m < CBD = m < ABD B EX 1) m <ZTF = 125 m <UTF = 50 Find m <ZTU Z U T D F 7 Intro Chapter 1.4 Angles.notebook EX 2) September 16, 2014 E C D F m < CDE= x+4 m<EDF=x+20. Find x= m<CDE m<EDF 8 Intro Chapter 1.4 Angles.notebook September 16, 2014 B A m < AOB = 3x + 12 m < BOC = 8x + 34 m < AOD = 6x + 114 Find x. EX 3) C D O 9 Intro Chapter 1.4 Angles.notebook September 16, 2014 Congruent angles Angles that have the exact same measure. Bisector Cuts an angle or a segment into two equal parts. EX. 4) BX bisects <ABC. If m<ABX = 5x, m<XBC = 3x+10, find x and m<ABC. A X B C 10 Intro Chapter 1.4 Angles.notebook September 16, 2014 11 Intro Chapter 1.4 Angles.notebook September 16, 2014 12 Intro Chapter 1.4 Angles.notebook September 16, 2014 13