1. Objectives:
Identify parallel and perpendicular lines
Identify the relationships of angles formed by parallel lines and a transversal

2. Line Relationships
Parallel Lines: are lines that are coplanar and do not intersect
Perpendicular Lines: are lines that are coplanar and intersect at a right angle

3. Angle Relationships
Complementary Angles - are two angles that add up to 90°
Supplementary Angles - are angles that add up to 180° (form a straight angle)
Vertical Angles - are the angles opposite each other when two lines cross.

4. Transversal
A transversal is a line that intersects two or more lines at different points
Line t is a transversal.

5. Parallel Lines cut by a Transversal
List the relationships you can see with the angles above.

6. Angles Formed by Transversals
Angles are corresponding angles if they occupy corresponding positions.

7. Corresponding Angles
When two parallel lines are cut by a transversal, the resulting corresponding angles are congruent.
So, in the figure above, if l || m, then ∠1 ≊∠ 2.
Source: hotmath.com

8. Angles Formed by Transversals
Angles are alternate exterior angles if they lie outside the parallel lines on opposite sides of the transversal.

9. Alternate Exterior Angles
When two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent.
So, in the figure above, if k || l, then: ∠1 ≊ ∠7 and ∠4 ≊ ∠6.
Source: hotmath.com

10. Angles formed by Transversals
Alternate interior angles lie on the inside of the parallel lines on opposite sides of the transversal.

11. Alternate Interior Angles
When two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.
So, in the figure above, if k || l, then ∠2 ≊ ∠8 and ∠3 ≊ ∠5.
Source: hotmath.com

12. Angles formed by Transversals
Consecutive interior angles lie inside of the parallel lines on the same side of the transversal.

13. Consecutive Interior Angles
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary.
So, in the figure above, if l || m, then ∠3 + ∠5 = 180° and
∠4 + ∠6 = 180°.