1.3b: Angles & Angle constructions - Angles and Rays

1.3b: Angles & Angle constructions- Angles and Rays Common Core State Standards for Mathematical Content Congruence G-CO Prove geometric theorems [Focus on validity of underlying reasoning while using variety of ways of writing proofs] G-CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).; copying an angle; bisecting an angle;

Rays • A ray extends forever in one direction • Has one endpoint • The endpoint is used first when naming the ray B ray R T ray W

Angles ( ) • Angles are formed by 2 non-collinear rays • The sides of the angle are the two rays • The vertex is where the two rays meet Vertex- where the rays meet ray ray

Naming an Angle You can name an angle by specifying three points: two on the rays and one at the vertex. • The angle below may be specified as ABC or ABC. The vertex point is always given in the middle. • Named: • ABC • CBA • B * • *you can only use the • vertex if there is ONE • angle Vertex

Ex. of naming an angle • Name the vertex and sides of 4, and give all possible names for 4. T X XW & XT WXT TXW 4 Vertex: Sides: Names: 4 5 W X Z

Angles • Measured in degrees • Congruent angles – angles that have equal measures m R = m S or R S

Congruent angles: Angles that have the same measure The arc marks are used to show that the two angles are congruent

Write a statement about the congruent angles NMP RMQ Or m NMP = m RMP

Name the angle shown as

Angles can be classified by their measures • Right Angles – 90 degrees • Acute Angles – less than 90 degrees • Obtuse Angles – more than 90, less than 180 • Straight Angles – 180 degrees

How to construct a congruent angle http://www.hstutorials.net/math/preAlg/php/php_09/php_09_07_x09.htm

Construct the bisector of an angle http://www.hstutorials.net/math/geometry/constructions/bisect_acute_angle.htm

1.3b: Angles & Angle constructions - Angles and Rays