1 / 8

Understanding Collinearity and Betweenness in Geometry

This lesson delves into the concepts of collinearity and betweenness of points in geometry. Collinear points lie on the same line, while non-collinear points do not. We also explore the importance of betweenness, which requires all points to be aligned on a straight path. Essential assumptions, such as the nature of straight lines, angles, and relative positions, are defined to help clarify geometric relationships. However, certain properties like right angles and congruence cannot be assumed without verification. Understanding these concepts is crucial for foundational geometry skills.

kapila
Télécharger la présentation

Understanding Collinearity and Betweenness in Geometry

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. Collinearity, Betweeness, and Assumptions Lesson 1.3

  2. Collinear: points on the same line Points ABC are collinear A B C Non-collinear: points that do not lie on the same line B A You can connect AB, AC, or BC, but ABC does not form a line. C

  3. Betweeness of Points: To have betweeness of points, all points must be on the same line. Z Y X Z is between Y and X Y Z X X is not “between” Y and Z

  4. Two possibilities with 3 points Collinear: all points are on the same line. Triangle : makes a triangle. Triangle Inequality The sum of two side lengths is always greater than the third side.

  5. Assumptions from diagrams: Can assume: Straight lines Straight angles Collinear points Betweenness of points Relative position of points

  6. Can’t Assume! Right angles Congruent segments Congruent angles Relative size of angles Relative size of segments

  7. Example: B D A C E Assume: AD and BE straight lines C, D, E non-collinear C is between B and E E is to the right of A

  8. B D A C Can’t Assume: <BAC is a right angle CD = DE <B = <E <CDE is obtuse BC is longer than CE E

More Related