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”.

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.

CORRESPONDING ANGLES

Corresponding Angles are angles that are in identical positions on separate parallel lines.  Therefore, they are congruent and equal.

VERTICAL ANGLES

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

ALTERNATE EXTERIOR and INTERIOR ANGLES

These angles are congruent or equal to each other.

SAME SIDE EXTERIOR and INTERIOR ANGLES

These angles are Supplementary to each other.

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