SAT-Style: Similar Triangles in Real Contexts

SAT Math · Axiom Academy

SAT-Style: Similar Triangles in Real Contexts Shadows, mirrors, and figures — three worked problems The SAT loves to wrap similar triangles in a real situation. The skill is always the same: spot the two similar triangles, line up corresponding sides, and solve one proportion. Here are the three setups you'll see most. The sun's rays hit both objects at the same angle, and both stand vertically, so the two right triangles (object + shadow) are similar by AA. Example 2 — Mirror on the Ground Light reflects at equal angles, so the triangle from the student's eye to the mirror is similar to the triangle from the mirror to the top of the tree (AA). Example 3 — A Parallel Cut Inside a Triangle Because , . Corresponding sides use the full side AB = AD + DB = 8 + 4 = 12 . Every problem above came down to a single proportion of corresponding sides. Identify the two similar triangles, write matching sides over matching sides, and cross-multiply.

This is the written version of the interactive lesson above. See the full SAT Math course.