Lines, Angles, and Triangles

SAT Math · Axiom Academy

The angle relationships the SAT leans on most — angle pairs, parallel lines cut by a transversal, and the rules every triangle obeys. Complementary, supplementary, and vertical angle pairs The eight angles formed when a transversal crosses parallel lines The triangle angle-sum rule and the exterior-angle theorem Isosceles triangles and how equal sides force equal angles Complementary — two angles that add to . Supplementary — two angles that add to (e.g. a straight line). Vertical angles — formed by two crossing lines; they are equal . Linear pair — adjacent angles on a line; they are supplementary. Two angles are supplementary. One measures 3x and the other 2x + 20 . Find x . Parallel Lines and a Transversal When a transversal crosses two parallel lines, the eight angles come in just two sizes. Matching positions are equal; the rest are supplementary. Corresponding angles are equal (same corner, different intersection). Alternate interior angles are equal (between the lines, opposite sides). Alternate exterior angles are equal. Same-side (co-interior) angles are supplementary — they add to . Lines are cut by a transversal. One angle measures . Find its corresponding angle and its same-side interior angle. Corresponding angles are equal: . Same-side interior angles are supplementary: . The angles of a triangle are in the ratio x : 2x : 3x . Find all three angles. The angles are — a right triangle.

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