Angle Transversals

When a line intersects two parallel lines, it creates several angles. These angles have specific relationships that are essential for solving problems related to lines and angles on the SAT.

Key Angle Relationships:

1. Corresponding Angles: Angles that are in the same position at each intersection are equal.
2. Alternate Interior Angles: Angles that are on opposite sides of the transversal and inside the two lines are equal.
3. Alternate Exterior Angles: Angles that are on opposite sides of the transversal and outside the two lines are equal.
4. Consecutive Interior Angles: Angles that are on the same side of the transversal and inside the two lines are supplementary (sum to 180 degrees).

Worked Example:

Consider two parallel lines cut by a transversal. Let angle 1 be $70^\circ$ and we want to find angle 2, which is an alternate interior angle to angle 1.

1. Identify the relationship: angle 1 and angle 2 are alternate interior angles.
2. Write the equation: angle 1 = angle 2.
3. Substitute the known value: $70^\circ = angle 2$.
4. Therefore, angle 2 is $70^\circ$.

Key Questions:

• What is the measure of an angle if its corresponding angle is $45^\circ$?
• If one of the consecutive interior angles measures $60^\circ$, what is the measure of the other angle?
• How do you find alternate exterior angles when given a transversal and two parallel lines?

Keywords:

• Transversal
• Corresponding angles
• Alternate interior angles
• Supplementary angles
• Parallel lines