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Applied Geometry

Applied Geometry. Lesson 3 – 4 Adjacent Angles and Linear Pairs of Angles. Objective: Learn to identify and use adjacent angles and linear pairs of angles. Adjacent Angles. Adjacent angles: Angles that share a common side and have the same vertex, but have no interior points in common.

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Applied Geometry

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  1. Applied Geometry Lesson 3 – 4 Adjacent Angles and Linear Pairs of Angles Objective: Learn to identify and use adjacent angles and linear pairs of angles.

  2. Adjacent Angles • Adjacent angles: • Angles that share a common side and have the same vertex, but have no interior points in common.

  3. Determine whether angles 1 and 2 are adjacent. No, angles do not share a vertex or side. No, do not share a common side Yes

  4. Determine whether angles 1 and 2 are adjacent. No, angles do not share a side. No, angles do not share a vertex.

  5. Determine whether angles 1 and 2 are adjacent. No, angles do not share a side. No, angles do not Share a vertex. Yes

  6. Determine whether the pair of angles are adjacent. A B Yes C E D No, can’t have one angle inside the other.

  7. Linear Pair • Linear Pair: • Two angles form a linear pair if and only if they are adjacent and their noncommon sides are opposite rays.

  8. Example • In the figure, CM and CE are opposite rays. • Name the angle that forms a linear pair with angle 1 • Do form a linear pair? Justify your answer. *Hint: what completes the 180 degrees or straight line No, they do not form a linear pair. The two angles do not add up to be 180 and do not create opposite rays.

  9. Your turn • Name the angle that forms a linear pair with • Tell whether form a linear pair. Justify your answer. Yes, they are adjacent and their noncommon sides are opposite rays.

  10. Your Turn • Name the angle that forms a linear pair with • Do form a liner pair? Justify your answer. No, they are not adjacent angles.

  11. Real world problem • The John Hancock Center in Chicago, Illinois, contains many types of angles. Describe the highlighted angles. The angles are adjacent and form a linear pair.

  12. Real World • Name examples of linear pairs in real world. (classroom etc.)

  13. Homework • Pg. 112 1 – 7 all, 8 – 26 E

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