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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 1 Name the Rays of the angle: BA What is the vertex of the angle? BC 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 Geometry is used to construct roofs. Use the diagram below to answer the following questions. G 1 2 H I F What is the vertex of the large angle? The vertex is G Name the Rays of the angle: GF , GH ,GI Name all the angles in the diagram using both letters & numbers. • 1 • 2 • FGI • IGF • IGH • FGH • HGI • HGF Measuring Angles and the Protractor Postulate Postulate 1-7 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. Four Different Classifications of Angles Right Angle Straight Angle Acute Angle Obtuse Angle Using a Protractor to Measure Angles 1. 2. 3. 4. Place the vertex at zero on the protractor Align one ray with the bottom edge of the protractor Read measurement (in degrees) on protractor 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 AXB and BXD form linear pairs and are adjacent angles G If the mDEG = 145º , find the mGEF. 145º + _____ 35 = 180 Name the adjacent angles? Are they a linear pair? D E F Suppose that m 1 = 42 and m ABC = 88. Find m 2. What postulate do you use to solve the problem? Use the Angle Addition Postulate to solve. m 1+m 2=m ABC Angle Addition Postulate. 42 + m 2 = 88 Substitute 42 for m m 2 = 46 Subtract 42 from each side. 1 and 88 for m ABC. Congruency of Angles and Triangles According to the diagram above, the following congruency statements are true: mA = mD, therefore AD mB = mE, therefore BE mC = mF, therefore CF Explain which angles and line segments are congruent by looking at the figures. Write congruency statements based on the statement ∆DEF ∆GHI.