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Applied Geometry

Learn to identify and apply adjacent angles and linear pairs. Explore concepts of angles sharing common sides and forming opposite rays. Practice determining adjacent angles and linear pairs in various scenarios. Real-world examples included.

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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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