Review

Geometry Concepts of Angles

Vertical Angles

• Definition: Vertical angles are the angles opposite each other when two lines intersect.

• Property: Vertical angles are equal.

• Example: Angles 1 and 4 are vertical angles.

Alternate Exterior Angles

• Definition: Alternate exterior angles are pairs of angles that lie outside the two parallel lines but on opposite sides of the transversal.

• Property: Alternate exterior angles are equal.

• Examples:
    - Angles 1 and 8 are alternate exterior angles.

Alternate Interior Angles

• Definition: Alternate interior angles are pairs of angles that lie between the two parallel lines, on opposite sides of the transversal.

• Property: Alternate interior angles are equal.

• Example:
    - Angles 3 and 6 are alternate interior angles.
    - Angles 2 and 7 are also alternate interior angles.

Corresponding Angles

• Definition: Corresponding angles are the angles that are in the same position at each intersection where a transversal crosses two lines.

• Property: Corresponding angles are equal.

• Example:
    - Angles 3 and 8 are corresponding angles.

Linear Pairs

• Definition: A linear pair is a pair of adjacent angles formed when two lines intersect. The angles are supplementary.

• Property: The angles in a linear pair sum to 180 degrees.

• Example:
    - Angles 7 and 8 are a linear pair, giving:
      $7 + 8 = 180$

Same Side Interior Angles

• Definition: Same side interior angles are pairs of angles that lie between the two parallel lines and are on the same side of the transversal.

• Property: Same side interior angles are supplementary, totaling 180 degrees.

• Example:
    - Angles 2 and 5 are same side interior angles, so:
      $2 + 5 = 180$

Same Side Exterior Angles

• Definition: Same side exterior angles are pairs of angles that lie outside the two parallel lines and are on the same side of the transversal.

• Property: These angles are supplementary as well.

• Example:
    - Angles 3 and 8 are identified as same side exterior angles.

Key Angle Properties

• All alternate angles (both alternate interior and alternate exterior) are congruent (equal).

• All same side angles (both same side interior and same side exterior) are supplementary (sum to 180 degrees).

Equations of Lines

• Overview: There are several forms of equations for lines, commonly used in geometry and algebra.

• Types of Line Equations:
    1. Slope Formula: Used to determine the steepness of a line.
    2. Slope-Intercept Form:
       - Formula: $y = mx + b$
         - where $m$ is the slope and $b$ is the y-intercept.
    3. Point-Slope Form:
       - Formula: $y - y_1 = m(x - x_1)$
         - where $(x_1, y_1)$ is a point on the line.

• Important Note: The slope formula appears on the formula sheet, but the other two forms do not.

Parallel Lines

• Definition: Parallel lines are lines that never intersect and are always the same distance apart.

• Property: Parallel lines have the same slope.

Additional Clarifications

• Example angles identified in exercises include:
    - Angle 1 and 4 as vertical
    - Angle 1 and 8 as alternate exterior angles
    - Angle 7 and 2 as alternate exterior angles
    - Angle 3 and 6 as alternate interior angles
    - Angle 7 and 8 forms a linear pair totaling 180 degrees
    - Angles 2 and 5 as same side interiors totaling 180 degrees.