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Lesson 1.4: Measure and Classify Angles

Lesson 1.4: 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. A. B. C. Ex. 1: Write 3 names for the angle shown. Then name the vertex and sides of the angle.

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Lesson 1.4: Measure and Classify Angles

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  1. Lesson 1.4: 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.

  3. A B C Ex. 1: Write 3 names for the angle shown. Then name the vertex and sides of the angle.

  4. Ex.2: Name the three angles in the diagram.

  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. A O B Postulate 3 Protractor Postulate: The measure of is equal to the absolute value of the difference between the real numbers for and .

  8. Use the diagram to find the measure of the indicated angle. Then classify the angle. EXAMPLE 3 Measure and classify angles b. <JHK b. <GHK c. <GHJ a. <GHL

  9. Postulate 4 Angle Addition Postulate: If P is in the interior of , then

  10. Ex 4 and 5: Find the indicated angle measure. R B Q 26° 76° 51° S C T A D m < QST = _____ m < QST = _____

  11. Ex.6: Given that , find and .

  12. Ex.7: Given that is a straight angle, find and .

  13. Ex.8: Given that is a right angle, find and .

  14. Congruent Angles: Two angles are congruent angles if they have the same measure.

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

  16. a° • b° • c° • d° • e° • f° Ex 10: Find the indicated angle measure. d° a° c° e° f° b° 103° 48°

  17. An angle bisector is a ray that divides an angle into two angles that are congruent. Ex.11: In the diagram below, bisects , and . Find the other two angle measures not given. .

  18. In the diagram BD bisects <ABC. Find m < ABC. D A (5x-11)° (4x+1)° C B

  19. Homework Pgs 28-30 #1, 3-10, 15-31, 33-38, 40-42

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