Geo/Trig - Quiz 11/30/22

**Types of Lines & Planes**

**Parallel Lines**: 2 lines on the same plane that never intersect

They are written as: ↔️AB || ↔️CD

**Parallel Planes:** 2 planes that never intersect

They are written as: plane a || plane b

**Skew Lines**: 2 lines on different planes that never intersect

**Angles Formed by a Transversal**

**Corresponding Angles**: Same side, same position

Example: Angles 1 and 3

**Alternate Interior Angles**: Different sides, on the inside

Example: Angles 2 and 6

**Alternate Exterior Angles**: Different sides, on the outside

Example: Angles 1 and 5

**Consecutive Interior Angles**: Same side, on the inside

Example: Angles 7 and 6

**Consecutive Exterior Angles**: Same side, on the outside

Example: Angles 1 and 4

**Classifying Slopes**

**Positive Slope**: ↗️

**Negative Slope**: ↘️

**Zero**: ↔️

**Undefined**: ↕️

**Slope Formulas**

**Using a Graph**: rise/run = m

**Using ordered pairs**: y2-y1/x2-x1 = m

**Transitive Property (TP)**

If two lines are parallel to the same line, they are parallel to each other

If p||q and q||r, then p||r

**Converses of Angle Theorems**

**Corresponding Angles Theorem**: If two parallel lines are cut by a transversal, then the pairs of __corresponding angles__ are __congruent__

**Converse**: If two lines are cut by a transversal so the __corresponding angles__ are __congruent__, then the lines are parallel

**Alternate Interior Angles Theorem**: If a transversal cuts two parallel lines, then the pairs of __alternate interior angles__ are __congruent__

**Converse**: If two lines are cut by a transversal so the __alternate interior angles__ are __congruent__, then the lines are parallel

**Alternate Exterior Theorem**: If two parallel lines are cut by a transversal, then the pairs of __alternate exterior angles__ are __congruent__

**Converse**: If two lines are cut by a transversal so the __alternate exterior angles__ are __congruent__, then the lines are parallel

**Consecutive Interior Angles Theorem**: If two parallel lines are cut by a transversal, then the pairs of __consecutive interior angles__ are __supplementary__

**Converse**: If two lines are cut by a transversal so the __consecutive interior angles__ are __supplementary__, then the lines are parallel

**Consecutive Exterior Angles Theorem**: If two parallel lines are cut by a transversal, then the pairs of __consecutive exterior angles__ are __supplementary__

**Converse**: If two lines are cut by a transversal so the __consecutive exterior angles__ are __supplementary__, then the lines are parallel

**Types of Lines & Planes**

**Parallel Lines**: 2 lines on the same plane that never intersect

They are written as: ↔️AB || ↔️CD

**Parallel Planes:** 2 planes that never intersect

They are written as: plane a || plane b

**Skew Lines**: 2 lines on different planes that never intersect

**Angles Formed by a Transversal**

**Corresponding Angles**: Same side, same position

Example: Angles 1 and 3

**Alternate Interior Angles**: Different sides, on the inside

Example: Angles 2 and 6

**Alternate Exterior Angles**: Different sides, on the outside

Example: Angles 1 and 5

**Consecutive Interior Angles**: Same side, on the inside

Example: Angles 7 and 6

**Consecutive Exterior Angles**: Same side, on the outside

Example: Angles 1 and 4

**Classifying Slopes**

**Positive Slope**: ↗️

**Negative Slope**: ↘️

**Zero**: ↔️

**Undefined**: ↕️

**Slope Formulas**

**Using a Graph**: rise/run = m

**Using ordered pairs**: y2-y1/x2-x1 = m

**Transitive Property (TP)**

If two lines are parallel to the same line, they are parallel to each other

If p||q and q||r, then p||r

**Converses of Angle Theorems**

**Corresponding Angles Theorem**: If two parallel lines are cut by a transversal, then the pairs of __corresponding angles__ are __congruent__

**Converse**: If two lines are cut by a transversal so the __corresponding angles__ are __congruent__, then the lines are parallel

**Alternate Interior Angles Theorem**: If a transversal cuts two parallel lines, then the pairs of __alternate interior angles__ are __congruent__

**Converse**: If two lines are cut by a transversal so the __alternate interior angles__ are __congruent__, then the lines are parallel

**Alternate Exterior Theorem**: If two parallel lines are cut by a transversal, then the pairs of __alternate exterior angles__ are __congruent__

**Converse**: If two lines are cut by a transversal so the __alternate exterior angles__ are __congruent__, then the lines are parallel

**Consecutive Interior Angles Theorem**: If two parallel lines are cut by a transversal, then the pairs of __consecutive interior angles__ are __supplementary__

**Converse**: If two lines are cut by a transversal so the __consecutive interior angles__ are __supplementary__, then the lines are parallel

**Consecutive Exterior Angles Theorem**: If two parallel lines are cut by a transversal, then the pairs of __consecutive exterior angles__ are __supplementary__

**Converse**: If two lines are cut by a transversal so the __consecutive exterior angles__ are __supplementary__, then the lines are parallel