Similar, Then Find

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 57 of 63.

Once two triangles are similar, their matching sides are in one ratio, so one known pair gives the others. The rule Similar triangles finds a side, and the board checks that the triangles really are similar: here AA from the parallel lines.

$Triangle ABC with DE parallel to BC; AD = 2, DB = 6, BC = 20, DE unknown$

The big triangle's side AB is 2 + 6 = 8, four times AD, so every side of △ABC is four times the matching side of △ADE. DE matches BC, so DE is 20 ÷ 4 = 5. The trap is using DB instead of AB: DB is not a side of the small triangle, and it does not match AD.