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Aim:

What are rays and angles?. Aim:. Ans. M(4, -8). Ans. 10. Do Now:. A ray is a part of a line that consists of an endpoint, and all points on one side of the endpoint. A. P. B. P. A. Def : Rays. Def: Opposite Rays.

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Aim:

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  1. What are rays and angles? Aim: Ans. M(4, -8) Ans. 10 Do Now: Geometry Lesson: Rays, Angles

  2. A ray is a part of a line that consists of an endpoint, and all points on one side of the endpoint. A P B P A Def: Rays Def: Opposite Rays Opposite Rays are two rays of the same line with a common endpoint and no other points in common. Geometry Lesson: Rays, Angles

  3. side A x B vertex C side Naming Angles: a) b) c) Def:Angle: An angle is the union of two rays having the same endpoint. Three capital letters, with vertex in the middle: Single lowercase letter or number inside the angle: Use the name of the vertex angle if it’s the only angle at that vertex: Geometry Lesson: Rays, Angles

  4. The measure of an angle is the number of degrees in the angle. A 25° B C are angles having equal measure. Q: Which of the following angles are congruent? C Ans. A) B) C) 45° 45° 45° A B Angle Measure: Def: Congruent Angles Geometry Lesson: Rays, Angles

  5. Straight angles have a measure of 180° A O B Def: Right Angle: A right angle has a measure of 90° P M Q Def: Straight Angle A straight angle is the union of two opposite rays. Geometry Lesson: Rays, Angles

  6. An acute angle has a measure greater than 0° and less than 90 °. X Y Z Def: Obtuse Angle: An obtuse angle has a measure greater than 90° and less than 180°. Q X R Def: Acute Angle: Geometry Lesson: Rays, Angles

  7. L m l H K J Def: Perpendicular Lines are two lines that intersect to form right angles. Are lines m and l perpendicular? NOT UNLESS SPECIFIED BY THE GIVEN INFO OR A BOX IN THE DIAGRAM !!!! Right Angles: Straight Angle: Geometry Lesson: Rays, Angles

  8. T P 20° 38° S R Addition/Subtraction of Angles: If several angles share a common vertex, we can write addition and subtraction expressions using the names of the angles. 20° + 38° = 58° 58° - 38° = 20° Geometry Lesson: Rays, Angles

  9. E 80° F G E P 40° A) Or 40° F B) C) G Def: Angle Bisector: The bisector of an angle is a ray that divides the angle into two congruent angles. Ans.: Make a ray from the vertex that divides it in half. Geometry Lesson: Rays, Angles

  10. M N P T R S Angle Bisector Examples Ex #1 a) State a pair of congruent angles. There is no way to tell from the given info. x = 4 Geometry Lesson: Rays, Angles

  11. A D B C Ex# 2 Simple 2-Column Proof: Given Def. of Angle Bisector Def. of Congruent Angles Geometry Lesson: Rays, Angles

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