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Understanding Angles: Postulates, Classification, and Measurement Techniques

In this lesson, students will learn about angles, their classifications, and measurement methods. Key terms include angle, vertex, congruent angles, acute, obtuse, right, and straight angles. Students will be introduced to important postulates such as the Angle Addition Postulate and Protractor Postulate. They will practice naming angles in various ways and will be able to classify them as acute, obtuse, right, or straight using specific criteria. Example problems will help reinforce their understanding and application of these concepts through hands-on assignments.

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Understanding Angles: Postulates, Classification, and Measurement Techniques

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  1. Objective: Students will be able to use angle postulates and classify angles. 1.4 Angles and Their Measures

  2. Vocabulary • Angle – formed by two rays connected with the same initial point. • Vertex – the “initial point” of an angle • Congruent Angles – two angles with the same degree measure • Interior – inside (of an angle)‏ • Exterior – outside • Acute Angle – angle between 0 and 90 • Obtuse Angle – angle between 90 and 180 • Right Angle – angle which = 90 • Straight Angle – angle which = 180 • Adjacent Angles – Angles which share a side and vertex

  3. Naming the angle • Three ways to name the angle: <B, < ABC, or <CBA. Vertex has to be in the middle. • Classify as acute/obtuse/right/straight • ACUTE • Name the vertex and sides • Vertex = B, Sides = BA, CB

  4. Postulates • Angle Addition Postulate – If D is inside < ABC, then <ABD + <DBC = <ABC • Protractor Postulate – when using a protractor, the measure of <WOY = to the positive difference of OW and OY

  5. Examples • Ex 1) If <ABD = 25 and <DBC = 57, what is <ABC? • 82 • Ex 2) If < ABC = 88 and <DBC = 33, what is <ABD? • 55

  6. Assignment • p. 29 1-22all, 26-28all, 35-37all, 54

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