21. Parallel Lines cut by a Transversal

A TRANSVERSAL is a line that intersects two or more lines at distinct points.

When a TRANSVERSAL intersects PARALLEL LINES, 8 angles are formed.

These angles have special realtionships that are helpful to remember.

• Corresponding Angles

• Vertical Angles

• Consecutive Interior Angles

• Consecutive Exterior Angles

• Alternate Interior Angles

• Alternate Exterior Angles

Just like corresponding parts of similar figures, CORRESPONDING ANGLES are in the same position on each parallel line.

These angle pairs are CONGRUENT.

And have the same degrees.

VERTICAL ANGLES are pairs of opposite angles formed by intersecting lines.

These angle pairs are CONGRUENT.

x and x are vertical angles and are the same degrees

y and y are vertical angles and are the same degreees

Angles in between the parallel lines (in the white area) are called INTERIOR ANGLES.

Angles that are outside of the parallel lines (in the blue areas) are EXTERIOR ANGLES.

CONSECUTIVE angles are on the SAME SIDE of the transversal.

ALTERNATE angles are on OPPOSITE SIDES of the transversal.

Angles on the SAME SIDE of the transversal and INSIDE of the parallel lines.

These angles are SUPPLEMENTARY ANGLES. (they add up to 180⁰)

Angles on the SAME SIDE of the transversal and OUTSIDE of the parallel lines.

These angles are SUPPLEMENTARY ANGLES.

Angles on the OPPOSITE SIDES of the transversal and INSIDE of the parallel lines.

These angles are CONGRUENT.

They have the same degrees.

Angles on the OPPOSITE SIDES of the transversal and OUTSIDE of the parallel lines.

These angles are CONGRUENT.

(They have the same degrees)

Angle Relationships and Parallel Lines

Day 2 - Parallel Lines and Transversals

We can use the relationships of these angle pairs to find the measure of missing angles.