1. 3-1 and 3-2: Parallel Lines and Transversals
Mr. Schaab’s Geometry Class
Our Lady of Providence Jr.-Sr. High School

2. Identifying Pairs of Lines
Two lines are:
Parallel if they do not intersect and are coplanar.
Perpendicular if they intersect to form right angles.
Skew if they do not intersect and are not coplanar.
(Note: ALL intersecting
lines are coplanar!)

3. Identifying Pairs of Lines - Example
In the cube below, identify the following:
A pair of perpendicular lines:
Line PS and Line PW
A pair of parallel lines:
Line PW and Line QX
Line PW and Line RY
Line QX and Line RY
A pair of skew lines:
Line PS and Line QX
Line PS and Line RY

4. Identifying Pairs of Planes - Example
In the cube below, identify the following:
A pair of perpendicular planes:
Plane SRY and Plane PWZ
Plane PQX and Plane QXY
A pair of Parallel planes:
Plane PQX and Plane SRY
Plane PWZ and Plane QRY
Plane PQR and WXY
Pair of skew planes:
None!

5. Angles and Transversals
Transversal – a line that intersects two or more coplanar lines at different points.
In the diagram on the right, line t is a the transversal of lines L1 and L2.
A transversal that intersects two lines forms 8 angles, all of which have special relationships.

6. Angle Relationships Corresponding Angles
Two angles that are in matching locations on different intersections.
∠1 and ∠5 are corresponding angles. 1 5

7. Angle Relationships Alternate Interior Angles
Two angles that lie between the two lines and on opposite sides of the transversal.
∠4 and ∠5 are alternate interior angles. 4 5

8. Angle Relationships Alternate Exterior Angles
Two angles that lie outside the two lines and on opposite sides of the transversal.
∠2 and ∠7 are alternate exterior angles. 2 7

9. Angle Relationships Consecutive Interior Angles
Two angles that lie between the two lines and on the same side of the transversal. These are also called “Same-side interior angles.”
∠3 and ∠5 are consecutive interior angles. 3 5

10. Angles and Transversals - Example
Identify all pairs of angles of the given type:
Corresponding:
∠1 & ∠5, ∠2 & ∠6, ∠3 & ∠7, ∠4 & ∠8
Alternate Interior:
∠2 & ∠7, ∠4 & ∠5
Alternate Exterior:
∠3 & ∠6, ∠1 & ∠8
Consecutive Interior:
∠4 & ∠7, ∠2 & ∠5 6 5 8 7 2 1 4 3

11. Parallel Lines and Transversals
Corresponding Angles Postulate:
If two parallel lines are cut by a transversal, then all pairs of corresponding angles are congruent.
∠1 ≅ ∠5 1 5

12. Parallel Lines and Transversals
Alternate Interior Angles Theorem:
If two parallel lines are cut by a transversal, then all pairs of alternate interior angles are congruent.
∠4 ≅ ∠5 4 5

13. Parallel Lines and Transversals
Alternate Exterior Angles Theorem:
If two parallel lines are cut by a transversal, then all pairs of alternate exterior angles are congruent.
∠1 ≅ ∠8 1 8

14. Parallel Lines and Transversals
Consecutive Interior Angles Theorem:
If two parallel lines are cut by a transversal, then all pairs of consecutive interior angles are supplementary.
m∠3 + m∠5 = 180° 3 5

15. Parallel Lines and Transversals
If you’re angle 3, then you have a lot of relationships! The other angles must really like you.
∠3 & ∠1 – Linear Pair (supplementary)
∠3 & ∠2 – Vertical Angles (congruent)
∠3 & ∠4 – Linear Pair (supplementary)
∠3 & ∠5 – Consecutive Interior Angles (supplementary)
∠3 & ∠6 – Alternate Interior Angles (congruent)
∠3 & ∠7 – Corresponding Angles (congruent)
∠3 & ∠8 – No relationship (∠8 is a jerk.) 1 2 3 4 5 6 7 8