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

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Presentation transcript:

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

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

Def:Angle: An angle is the union of two rays having the same endpoint. side B A C x vertex Naming Angles: a) b) c) 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

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

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

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

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

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

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

Angle Bisector Examples a) State a pair of congruent angles. There is no way to tell from the given info. x = 4 Geometry Lesson: Rays, Angles

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