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Bellringer

Bellringer. Your mission: Construct a perfect square using the construction techniques you have learned from Unit 1. You may NOT measure any lengths with your ruler. You may NOT measure any angles

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Bellringer

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  1. Bellringer • Your mission: • Construct a perfect square using the construction techniques you have learned from Unit 1. • You may NOT measure any lengths with your ruler. • You may NOT measure any angles • All sides must be perfectly perpendicular (90 degree angle) and all side segments must be congruent (hint hint ;) • You have 10 minutes.

  2. Unit 2 Angle Pairs ? 2 3 Unit 2: This unit introduces angles, types of angles, and angle pairs. It defines complimentary and supplementary angles. 4 1 5

  3. Standards • SPI’s taught in Unit 2: • SPI 3108.1.1 Give precise mathematical descriptions or definitions of geometric shapes in the plane and space. • SPI 3108.1.4 Use definitions, basic postulates, and theorems about points, lines, angles, and planes to write/complete proofs and/or to solve problems. • SPI 3108.3.1 Use algebra and coordinate geometry to analyze and solve problems about geometric figures (including circles). • SPI 3108.4.2 Define, identify, describe, and/or model plane figures using appropriate mathematical symbols (including collinear and non-collinear points, lines, segments, rays, angles, triangles, quadrilaterals, and other polygons). • CLE (Course Level Expectations) found in Unit 2: • CLE 3108.1.1 Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning. • CLE 3108.4.1 Develop the structures of geometry, such as lines, angles, planes, and planar figures, and explore their properties and relationships. • CFU (Checks for Understanding) applied to Unit 2: • 3108.1.7 Recognize the capabilities and the limitations of calculators and computers in solving problems. • 3108.4.5 Use vertical, adjacent, complementary, and supplementary angle pairs to solve problems and write proofs.

  4. Review • We have already addressed much of what is covered in the section on angles • We classify angles in 4 ways: • Less than 90 degrees: • Acute Angle • Equal to 90 degrees: • Right angle • Greater than 90, but less than 180: • Obtuse angle • Equal to 180 degrees: • Straight angle

  5. Review • We define an angle bisector as: • An angle bisector is a ray that divides an angle into two congruent coplanar angles. Its endpoint is the angle vertex. • You can also say that a ray or segment bisectsthe angle.

  6. Angle Pairs –Vertical Angles • Vertical Angles: Two angles whose sides are opposite rays • Which angle pairs are vertical angles? • Angle A and Angle C • Angle D and Angle B • What letter in the alphabet always creates vertical angles? Vertical Angles are ALWAYS equal A D B C

  7. Angle Pair –Complementary Angles • Complementary Angles –Two angles whose measures have a sum of 90 degrees • Each angle is called the complement of the other • Angle 1 is the complement of angle 2 • Angle B is the complement of Angle A. What conclusion can we draw? • Angle B is 30 degrees 2 B 1 60 A

  8. Angle Pairs –Adjacent Angles • Adjacent Angles – Two coplanar angles with one common side, one common vertex, and no common interior points Common Vertex A B Common Side 1 2

  9. Angle Pairs –Supplementary Angles These are also known as “Linear Pairs” because they make a line • Supplementary Angles –Two angles whose measures have a sum of 180 degrees • Each angle is called the supplement of the other • The angles do not have to be touching, or share a vertex, to be supplementary. They just have to sum 180 degrees. A B 45 135

  10. Example • Identify the given angle pairs • Complementary Angles • Supplementary Angles • Vertical Angles • Adjacent Angles 2 1 3 5 4

  11. Conclusions • Given the type of diagram we have seen, you can conclude that angles are: • Adjacent Angles • Vertical Angles • Adjacent supplementary Angles • Without congruency marks, you cannot conclude that: • Angles or segments are congruent • An angle is a right angle • Lines are parallel or perpendicular • Adjacent angles are complementary

  12. Example • What conclusions can we make about this diagram? 2 3 4 1 5

  13. Vertical Angle Theorem • Vertical Angles are Congruent • If angle ABC = 120 degrees, what is the measure of angle EBD? • What is the measure of angle CBD? • What is the measure of angle ABE? A C 120 B D E

  14. Example • Solve for X • Since they are equal in measure, we set them equal to each other: 4X = 3X + 35 • Therefore X = 35 4X 3X+35

  15. Assignment • Text, Page 38-39 problems 7-30, 33-36 (guided practice) • Worksheet P 1-5 • Worksheet 2-5 • Angles and Segments Worksheet • IF YOU DO NOT USE THE ANGLE SYMBOL, THEN I WILL MARK -3 ON YOUR PAPER. LABEL PROPERLY!

  16. Unit 2 Bellringer (2 points each) • In your own words –in other words, don’t copy your notes word for word- define: • Vertical Angles • Adjacent Angles • Supplementary Angles • Complementary Angles • Linear Angles

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