Angle Relationships | Parallel Lines cut by a Transversal
PARALLEL LINES cut by a TRANSVERSAL
The Transversal is the diagonal line that crosses a set of Parallel Lines. Do you see the arrows on the two horizonal lines? This is a visual signal that the lines are parallel. You don’t even need the label “Parallel Lines”.

The area inside of the Parallel Lines is the Interior, and above and below the pair of lines is the Exterior.
ANGLE RELATIONSHIPS
Students must understand the relationships between the angles. It is foundational knowledge that directly relates to 2-Dimensional and 3-Dimensional objects. In Florida, it is a major cluster in Geometry (MAFS.912.G-CO). In regards to Common Core (CCSS 8.G.A.5), it appears to be an 8th Grade Standard as found here, and here at Khan Academy.
Parallel Lines cut by a Transversal create two categories of angle relationships: Supplementary (angles add up to 180 degrees) and Congruent/Equal to each other.
LINEAR PAIRS
Linear Pairs form a straight line, and are Supplementary.

Linear Pairs form a Line
CORRESPONDING ANGLES
Corresponding Angles are angles that are in identical positions on separate parallel lines. Therefore, they are congruent and equal.

Corresponding Angles
VERTICAL ANGLES
Vertical Angles positionally are opposite of each other, and congruent or equal.

Vertical Angles
ALTERNATE EXTERIOR and INTERIOR ANGLES
These angles are congruent or equal to each other.

Alternate Exterior

Alternate Interior
SAME SIDE EXTERIOR and INTERIOR ANGLES
These angles are Supplementary to each other.

Same Side Exterior

Same Side Interior
Students often need manipulatives to better understand math, especially Geometry. I love using Patty Paper.
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What is it? It’s the square wax paper sheets that keep hamburger patties from sticking to each other. How do I use it? Stay tuned, and you’ll learn how to prove angle relationships with it.
Would you like a printable of these images? Please email me at mrs@mrandmrsmath.com.
Mrs Math