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Chapter 1.4 Notes: Measure and Classify Angles

Chapter 1.4 Notes: Measure and Classify Angles. Goal: You will name, measure, and classify angles. . An angle consists of two different rays with the same endpoint. The rays are the sides of the angle. The endpoint is the vertex of the angle.

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Chapter 1.4 Notes: Measure and Classify Angles

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  1. Chapter 1.4 Notes: Measure and Classify Angles Goal: You will name, measure, and classify angles.

  2. An angle consists of two different rays with the same endpoint. • The rays are the sidesof the angle. • The endpoint is the vertex of the angle. • Name the angle above: _____, ______, ______ • ____________ is the vertex of the angle.

  3. Ex.1: Name the three angles in the diagram.

  4. Ex.2: Name the three angles in the diagram. M O N P

  5. Classifying Angles: • Angles can be classified as acute, right, obtuse, and straight. • Acute angles have a measure greater than 0 and less than 90. • Right angles have a measure of 90. • Obtuse angles have a measure greater than 90 and less than 180. • Straight angles have a measure of 180.

  6. Measuring Angles: • A protractor can be used to approximate the measure of an angle. • An angle is measured in units called degrees (o).

  7. Postulate 3 Protractor Postulate: Consider and a point A on one side of . The rays of the form can be matched one to one with the real numbers from 0 to 180. The measure of is equal to the absolute value of the difference between the real numbers for and . A O B

  8. Use the diagram to find the measure of the indicated angle. Then classify the angle. a.KHJ b. GHK c. GHJ d. GHL EXAMPLE 3 Measure and classify angles SOLUTION A protractor has an inner and an outer scale. When you measure an angle, check to see which scale to use.

  9. Postulate 4 Angle Addition Postulate: If P is in the interior of , then the measure of is equal to the sum of the measures of and . If P is in the interior of , then

  10. Ex.4: Given that , find and .

  11. Ex.5: If find and

  12. Ex.6: Given that is a straight angle, find and .

  13. Ex.7: Given that is a right angle, find and .

  14. Congruent Angles: • Two angles are congruent angles if they have the same measure. Angle measures ar equalAngles are congruent

  15. Ex.8: The photograph shows some of the angles formed by the ropes in a trapeze apparatus. Identify the congruent angles. If , what is ?

  16. Ex.9: Use the diagram below. a. Identify all pairs of congruent angles. b. , , and . Find the other angle measures in the diagram.

  17. An angle bisector is a ray that divides an angle into two angles that are congruent. Ex.10: In the diagram below, bisects , and . Find .

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