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Understanding Angles: Adjacent, Complementary, and Supplementary Angles Explained

Welcome to class! Today's lesson focuses on measuring angles and their properties. Begin by gathering your materials: patty paper, protractor, and notes. You will draw adjacent angles that share a vertex and ray but do not overlap. We'll explore concepts like the Angle Addition Postulate, where the sum of two angles may equal the measure of another angle. Learn about complementary and supplementary angles, including definitions, examples, and the Linear Pair Property. Get ready to engage and test your understanding with whiteboards.

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Understanding Angles: Adjacent, Complementary, and Supplementary Angles Explained

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Presentation Transcript

  1. Welcome to class The warm up is Lesson 1.2 on the back table

  2. 5 6 8 22 28 4 Does not make sense. No such notation. Does not make sense. A segment + a number does not equal a number

  3. Let’s grade your homework

  4. Measuring Angles Please get: One piece of patty paper Protractor Your notes

  5. With the straight edge, draw these angles on your patty paper (DO NOT FREE HAND): S R P Q CONGRATULATIONS!! You have just created your first set of ADJACENT ANGLES. ADJACENT ANGLES share a vertex and a ray but they can’t overlap. m>PQS = m>SQR = m>PQR = Measure each angle. Do you notice anything?

  6. S P R Q Which one makes sense? B A Angle Addition Postulate mPQS + m  SQR = m  PQR  A +  B = 85° Or m A + m B = 85°

  7. Angle Congruence Postulate • If two angles have the same measure, then they are congruent. • the converse is also true: If two angles are congruent, then they have the same measure. Can you write a biconditional?

  8. Are you doing ok? • COMPLEMENTARY Angles – Exactly two angles whose sum is 90°. Each angle is a COMPLEMENT of the other. • SUPPLEMENTARY Angles = Exactly two angles whose measure is 180°. Each angle is a SUPPLEMENT of the other. 30° B 120° C A 60° Complementary angles are  A and  B  A and  B are complements of each other  A and  C are supplementary angles  A and  C are supplements of each other

  9. Linear Pair Property If two angles form a line, they are a linear pair AND are supplementary. 125° 55°

  10. Angles RIGHT ANGLE = 90° INDICATED BY THE BOX IN THE CORNER ACUTE ANGLE = angle less than 90° OBTUSE ANGLE = angle more than 90° but less than 180° STRAIGHT ANGLE = angle that equals 180° REFLEX ANGLE = angle greater than 180° and less than 360°.

  11. Whiteboards Please get a whiteboard, marker, and eraser. Doodle time starts in one minute.

  12. Your assignment 3.1 Packet

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