Geometry Objectives & Learning Targets 1.0 - 3.0

1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning.

2.0 Students write geometric proofs, including proofs by contradiction.

3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement.


Learning Targets:

  1. I can identify the undefined terms - point, line, and plane.
  2. I can give examples of a point, line, or plane.
  3. I can name Points, Lines, Planes, Segments, Rays, and Angles.
  4. I can identify and give examples of axioms/postulates, theorems, and their corollaries.
  5. I can identify and understand how to apply Foundational Definitions - length, angle measure.
  6. I know the definition of Inductive Reasoning and can show examples of Inductive Reasoning.
  7. I know the definition of Deductive Reasoning and can show examples of Deductive Reasoning.


Vocabulary:

  1. Segment
  2. Endpoints
  3. Ray
  4. Angle
  5. Vertex of the Angle
  6. Sides of the Angle
  7. Acute Angle
  8. Right Angle
  9. Obtuse Angle
  10. Complementary Angles
  11. Supplementary Angles
  12. Collinear
  13. Coplanar
  14. Naming Points, Lines, Planes, Segments, Rays, Angles
  15. Intersection
  16. Postulates (also known as Axioms)
  17. Conjecture
  18. Equidistant
  19. Equiangular

Definitions:

  1. Definition Segment
  2. Definition of Length
  3. Definition of Ray
  4. Definition of Angle
  5. Definition of Angle Measure
  6. Definition of Parallel Lines
  7. Definition of Perpendicular Lines
  8. Definition of Segment Bisector
  9. Deinition of Midpoint
  10. Definition of Perpendicular Bisector
  11. Definition of Angle Bisector


Properties:

  1. Linear Pair Property

Postulates:

  1. The intersection of two lines is a point.
  2. The intersection of two planes is a line.
  3. Through any two points there is exactly one line.
  4. Through any three noncollinear points there is exactly one plane.
  5. If two points are in a plane, then the line containing them is also in the plane.
  6. Segment Congruence Postulate
  7. Segment Addition Postulate
  8. Angle Congruence Postulate
  9. Angle Addition Postulate