modules 1 and 2 math

Mind Map: Geometry Concepts

Central Idea: Geometry Concepts

1. Basic Elements

• Point

  • Definition: A location in space with no dimensions.

  • Ex. Point A

• Plane

  • Definition: A flat surface extending infinitely in all directions.

  • Ex. Plane M

• Space

  • Definition: The boundless three-dimensional extent to which objects exist.

2. Relationships

• Collinear

  • Definition: Points that lie on the same straight line.

  • Ex.

    

  Coplanar

  • Definition: Points that lie on the same plane.

  • Ex.

    

3. Congruence

• Congruent

  • Definition: Figures that have the same shape and size.

  • Ex.

    

4. Distance

• Distance Formula

  • Formula: ( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} )

• Finding Distance on a Number Line

  • Formula: ( |x_2 - x_1| )

5. Midpoint and Bisectors

• Midpoint

  • Definition: The point that divides a segment into two equal parts.

  • Ex.

    

• Midpoint Formula: x_1+x_2/2

  Bisect

  • Definition: To divide into two equal parts.

• Segment Bisector

  • Definition: A line, ray, or segment that divides another segment into two equal parts.

  • Ex.

    

6. Rays and Angles

• Ray

  • Definition: A part of a line that starts at a point and extends infinitely in one direction.

  • Ex.

    

  Opposite Rays

  • Definition: Two rays that share a common endpoint and extend in opposite directions. Has a measure of 180 degrees. Forms a straight angle.

  • Ex.

    

• Straight Angle

  • Definition: An angle that measures 180 degrees. Opposite rays form this.

7. Angle Properties

• Angle

  • Definition: Formed by two rays with a common endpoint (vertex).

  • 

  Sides

  • Definition: The rays that form the angle.

  • Ex.

    

• Vertex

  • Definition: The common endpoint of the rays.

• Interior

  • Definition: The space inside the angle.

  • Ex.

    

  Exterior

  • Definition: The space outside the angle.

  • Ex.

    

8. Angle Relationships

Congruent Angles

• Definition: Angles that have the same measure.

• Ex.

  

Angle Bisector

• Definition: A ray that divides an angle into two equal angles.

• Ex.

  

9. Special Angle Pairs

Adjacent Angles

• Definition: Two angles that lie in the same plane, have a common vertex and a common side, but have no common interior points.

• Ex.

  

Linear Pair

• Definition: A pair of adjacent angles with noncommon sides that are opposite rays.

• The sum of the angle measures 180 degrees

• Ex.

  

Vertical Angles

• Definition: The two nonadjacent angles formed by two intersecting lines

• Vertical angles are congruent

•