Do Now

1. Do Now • Think about the marshmallow challenge we did yesterday, as well as our discussion afterwards. Answer the following questions in your notebook. • What is a goal? • Why do we need goals? • What characteristics should a goal have?

2. Personal goals • Stand up if… • You want to go to college. • You want to work in a health career. • You want to be a teacher. • You want to work in masonry, carpentry, or auto mechanics. • You want to play sports. • You want to pass this class.

3. “I hope you…” letters • Write a letter to future self. Start each sentence with “I hope you…” • Complete the sentence with your dreams and goals for this class and for the future. • Write at least a page. • I’ll give you back your letters at the end of the semester. 

4. Do Now • In your notebook, define the following words. • Wind • Soft • Kind • Love

5. Unit 1: Basics of Geometry and Transformations 1.1 Points, Lines, and Planes

6. Think back to the words I asked you to describe in the Do Now… wind, soft, kind, and love. • Why were these words hard to define? • When you wrote your “definitions”, were you really defining in the truest sense?

7. Using Undefined Terms and Definitions • To define a word is to state or set forth the meaning of a word. • For example, the definition of cat is “a small domesticated carnivore.” • In geometry, some words, such as point, line, and plane, are undefined terms. There are no formal definitions for these words. • But we still have to understand what these words mean… so what do we do? • We learn about what these terms are and what they do based on their descriptions.

10. Using Undefined Terms and Definitions

11. Using Undefined Terms and Definitions • A few more basic concepts in geometry must also be commonly understood without being defined. • One such concept is the idea that a point lies on a line or a plane. • Collinear points are points that lie on the same line. • Coplanar points are points that lie on the same plane.

12. Naming Collinear and Coplanar Points • Name three points that are collinear. • Name four points that are coplanar. • Name three points that are not collinear.

13. Using Undefined Terms and Definitions • Another undefined concept in geometry is the idea that a point on a line is between two other points on the line. • You can use this idea to define other important terms in geometry.

14. Consider the line AB (symbolized by AB ). • The line segment or segment AB (symbolized by AB ) consists of the endpoints of A and B, and all points on AB that are between A and B.

15. The ray AB (symbolized by AB) consists of the initial point A and all the points on AB that lie on the same side of A as point B. • Note that AB is the same as BA, and AB is the same as BA. However, AB and BA are not the same. They have different endpoints and extend in different directions. • If C is between A and B, then CA and CB are opposite rays.

16. Like points, segments and rays are collinear if they lie on the same line. • So, would opposite rays be collinear? • Segments, rays, and lines are coplanar if they lie on the same plane.

17. Parallel Lines and Planes • Two lines are parallelif they are in the same plane AND they do not intersect. • Planes can also be parallel. • Example: The shelves in a bookcase. • Two planes are parallel if they do not intersect.

18. Perpendicular Lines and Planes • Two lines are perpendicularif they intersect at a 90 degree angle. • Planes can also be perpendicular. • Example: A book standing upright on a bookshelf. • Plane A is perpendicular to plane B if Plane A contains a line that is perpendicular to Plane B.

19. Drawing Lines, Segments, and Rays • Draw three non-collinear points, J, K, and L. • Then draw JK, KL, and LJ.