Part 13 · Ten original questions
Advanced Similar Triangle Systems
Identify similar triangles, establish the scale factor, then find whole lengths, missing segments and algebraic lengths. Questions become progressively harder.
Method reminder
Match the shared vertex first, then the right-angle corners. The triangles share one angle and each has a right angle; derive the third using the 180° angle sum. All three corresponding angles match: similar by AAA. Use large ÷ small for the scale factor. A whole side is the sum of its segments; do not compare a segment with a whole corresponding side.
Diagrams are original and not drawn to scale. Use the stated lengths. Questions 8–10 require algebra. Worked solutions do not mark a question complete. Work is saved only on this browser profile.