1 / 12

Understanding Angles and Rays: Geometric Constructions and Theorems

Dive into the fundamentals of angles and rays with this comprehensive guide focusing on geometric constructions and theorems. Explore how angles are formed by two non-collinear rays, learn to name angles using vertex points, and understand the classification of angles based on their measures (acute, right, obtuse, and straight). Additionally, this resource covers the methods for congruent angle constructions using various tools, including compass and straightedge. Perfect for students and educators alike, this guide emphasizes the reasoning behind geometric proofs.

sai
Download Presentation

Understanding Angles and Rays: Geometric Constructions and Theorems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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;

  2. 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

  3. 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

  4. 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

  5. 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

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

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

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

  9. Name the angle shown as

  10. 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

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

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

More Related