Section 1-4: Measuring Angles SPI 32A: Identify properties of plane figures from information in a diagram Objective: Classify and find the measure of angles.

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Presentation transcript:

Section 1-4: Measuring Angles SPI 32A: Identify properties of plane figures from information in a diagram Objective: Classify and find the measure of angles Angle Formed by two rays with the same endpoint. Rays Vertex (endpoint)

Naming Angles Name the Rays of the angle: What is the vertex of the angle? Vertex is B Different ways to name the angle: Name by vertex:  B Name by 3 points (vertex in middle):  ABC or  CBA Name by a number:  1 1

Geometry is used to construct roofs. Use the diagram below to answer the following questions. F G H 12 What is the vertex of the large angle? Name all the angles in the diagram using both letters & numbers. Name the Rays of the angle: The vertex is G I  1  2  FGI  IGF  IGH  HGI  FGH  HGF

Protractor Postulate For every angle, there corresponds a number between 0 and 180º. This number is called the measure of the angle and is written in degrees. Postulate 1-7 Measuring Angles and the Protractor Postulate

Four Different Classifications of Angles Right AngleStraight Angle Acute AngleObtuse Angle

Using a Protractor to Measure Angles 1. Place the vertex at zero on the protractor 2. Align one ray with the bottom edge of the protractor 3. Read measurement (in degrees) on protractor 4. Caution: Pay attention to the numbers Ensure answer makes sense What type of angle is represented in the diagram?

Angle Addition Postulate Postulate 1-8 Angle Addition Postulate If the m  DEG = 145º, find the m  GEF. D E F G 145º + _____ =  AXB and  BXD form linear pairs and are adjacent angles Name the adjacent angles? Are they a linear pair?

Use the Angle Addition Postulate to solve. m 1 + m 2 = m ABCAngle Addition Postulate m 2 = 88Substitute 42 for m 1 and 88 for m ABC. m 2 = 46Subtract 42 from each side. Suppose that m 1 = 42 and m ABC = 88. Find m 2. What postulate do you use to solve the problem?

Congruency of Angles and Triangles According to the diagram above, the following congruency statements are true: m  A = m  D, therefore  A  D m  B = m  E, therefore  B  E m  C = m  F, therefore  C  F Explain which angles and line segments are congruent by looking at the figures. Write congruency statements based on the statement ∆ DEF  ∆ GHI.