What Is the Same Side Interior Angles Theorem?


Quick Answer

The same-side interior angles theorem states that two same-side interior angles are supplementary when two parallel lines are intersected by the transverse line. Same-side interior angles are two angles that are on the same side of the transverse line and on the interior of the two parallel lines. The three lines form eight angles, four surrounding each intersecting line.

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Full Answer

Supplementary angles, when their degree measurements are added together, total 180 degrees. For instance, two same-side interior angles can measure 120 and 60 degrees, or their values can be algebraic expressions, such as (2x + 43) and (2x - 3).

Likewise, four pairs of two angles in this set are congruent, meaning they have the same measurements. All four angles that meet add up to 360 degrees. Opposite angles, or alternate angles, have the same value, except they open in opposite directions of the intersected lines. A transverse line, or transversal, is a line that intersects two or more other lines in the same plane.

Real-world applications of this theorem include city planning, parking lot layouts, angles of wooden beams in a house and window panes with intersecting lines. City streets intersect at parallel angles, and construction crews must take angles into account when building sidewalks and infrastructure improvements around an intersection.

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