Lines and Angles
Lessons in this chapter
About Lines and Angles
Lines and Angles extends 7th grade's basic angle relationships to the specific case of parallel lines cut by a transversal, then applies angle reasoning to triangles, polygons, and similarity.
Parallel Lines and Transversals introduces the specific angle pairs created when a line crosses two parallel lines, corresponding, alternate interior, and alternate exterior angles: all of which turn out to be either equal or supplementary.
Angles of Triangles revisits the triangle angle sum property from a transversal argument (drawing a parallel line through one vertex), while Angles of Polygons extends the same reasoning to find the angle sum of any polygon by breaking it into triangles.
Using Similar Triangles closes the chapter by applying angle relationships to prove two triangles similar, then using that similarity to find missing side lengths, connecting straight back to the Similarity and Transformations work from the previous chapter.
Each of the four lessons is an 8th grade math worksheet worked in the page: Parallel Lines and Transversals, Angles of Polygons and Using Similar Triangles are practice questions on real diagrams rather than a list of angle rules. The per question marking catches a misnamed angle pair before it is used to solve for the next unknown. All four are free to try, with no login needed for your first 3.
Frequently asked questions
Parallel Lines and Transversals opens the chapter with corresponding, alternate and co-interior angles and the equalities a transversal creates. Angles of Triangles revisits the 180 degree sum and the exterior angle result, Angles of Polygons generalizes it to the interior and exterior angle sums of any polygon, and Using Similar Triangles applies angle matching to prove triangles similar and find missing side lengths, including the slope argument behind linear graphs. This sits in the Common Core domain Geometry (8.G).
Corresponding angles (same position at each intersection) are equal, alternate interior angles (between the parallel lines, on opposite sides of the transversal) are equal, and co-interior angles (between the lines, same side) are supplementary.
Identify which angle relationship applies, corresponding or alternate angles are equal, so set the missing angle equal to its given pair; co-interior angles are supplementary, so subtract the given angle from 180°.
Angles of Triangles proves the same 180° angle sum from 7th grade using a transversal argument, drawing a line through one vertex parallel to the opposite side, rather than just stating the rule, connecting it directly to Parallel Lines and Transversals.
Angles of Polygons has kids split a polygon into triangles by drawing diagonals from one vertex, then multiply the number of triangles by 180°: a pentagon splits into 3 triangles, so its angles sum to 540°.
Using Similar Triangles has kids first prove two triangles similar using angle relationships (like corresponding angles from parallel lines), then set up a proportion between corresponding sides to solve for an unknown length.