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Warm Up

Learn Euclidean & Non-Euclidean Geometry, differentiate undefined terms, and explore collinear & coplanar points. Discover concepts of rays, opposite rays, and intersections in geometry. Practice and discuss intersections of lines and planes. Understand postulates, conjectures, and theorems in geometric reasoning.

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Warm Up

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  1. Warm Up Name all points on the Coordinate Plane and Note their Corresponding Quadrant or Axis..

  2. Euclidean and Non Euclidean Geometry! So what’s the difference?

  3. What do we know about it?

  4. What do we know about it?

  5. And..

  6. Undefined Terms Words that do not have formal definitions but there is an agreement about what they mean.

  7. Point

  8. Line

  9. Plane

  10. Think, Pair, Share • Discuss what Points, Lines, and Planes are and explain what an undefined term is.

  11. Collinear Points

  12. Coplanar Points

  13. Think, Pair, Share • What does it mean to be Collinear or Coplanar?

  14. a. Give two other names for PQand for plane R. b.Name three points that are collinear. Name four points that are coplanar. • Other names for PQare QPand line n. Other names for plane Rare plane SVT and plane PTV. EXAMPLE 1 Name points, lines, and planes SOLUTION

  15. EXAMPLE 1 Name points, lines, and planes b. Points S, P, and Tlie on the same line, so they are collinear. Points S, P, T,and Vlie in the same plane, so they are coplanar.

  16. 1. Use the diagram in Example 1. Give two other names for ST. Name a point that is not coplanar with points Q, S, and T. ANSWER TS, PT; point V Think, Write, Pair, Share GUIDED PRACTICE

  17. Defined Terms Terms that can be described using known terms like Point or Line

  18. Segment

  19. Ray

  20. Opposite Ray

  21. a. Give another name for GH . a. Another name for GHis HG . b. The rays with endpoint Jare JE, JG, JF, and JH . The pairs of opposite rays with endpoint Jare JEand JF, and JGand JH. EXAMPLE 2 Name segments, rays, and opposite rays b. Name all rays with endpoint J . Which of these rays are opposite rays? SOLUTION

  22. 2. Give another name for EF ANSWER FE 3. Are HJand JH the same ray ? Are HJand HGthe same ray? Explain. ANSWER No; the rays have different endpoints.Yes; points J and G lie on the same side of H. Think, Write, Pair, Share GUIDED PRACTICE

  23. Intersection

  24. c. a. b. EXAMPLE 3 Sketch intersections of lines and planes a. Sketch a plane and a line that is in the plane. b.Sketch a plane and a line that does not intersect the plane. c. Sketch a plane and a line that intersects the plane at a point. SOLUTION

  25. STEP 1 Draw: a vertical plane. Shade the plane. STEP 2 Draw: a second plane that is horizontal. Shade this plane a different color. Use dashed lines to show where one plane is hidden. STEP 3 Draw: the line of intersection. EXAMPLE 4 Sketch intersections of planes Sketch two planes that intersect in a line. SOLUTION

  26. Think, Pair, Share • What does ‘defined’ mean? Discuss the differences between Rays, Opposite Rays, and Intersections.

  27. Quick Write • In at least three sentences, compare and contrast points, lines, and planes.

  28. Postulate- a statement that is accepted as true without proof. • Through any two points there is exactly one line. • Through any three non-collinear points there is exactly one plane containing them • If two points lie in a plane, then the line containing those points is on the plane • If two lines intersect, then they intersect in exactly one point • If two planes intersect, then they intersect in exactly one line. • Conjecture- A statement you believe to be true based on inductive reasoning. • Theorem- a statement that can be proven true.

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