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”.
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 form a straight line, and are Supplementary.
Corresponding Angles are angles that are in identical positions on separate parallel lines. Therefore, they are congruent and equal.
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.
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