How to Solve Detour Proofs in Geometry

The Organic Chemistry Tutor

This video provides an in-depth tutorial on how to construct "detour proofs" in geometry, a specific type of proof where students must prove two sets of triangles are congruent to reach a final conclusion. The video breaks down the logical structure of these multi-step problems, explaining that immediate information is often insufficient to prove the desired statement directly. Instead, a "detour" is required—proving an intermediate set of triangles congruent to gather necessary information (usually via CPCTC) for the final proof. The content covers two complex examples. The first involves a kite-shaped figure requiring the SSS postulate followed by the SAS postulate. The second example tackles a more challenging diagram with overlapping triangles, requiring students to separate the figures visually, apply the Segment Addition Postulate to find congruent segments, and use the AAS theorem. The narrator models the thought process of a mathematician, demonstrating how to strategize before writing and how to set up a formal two-column proof. This resource is highly valuable for high school geometry classrooms as it explicitly models the metacognitive strategies needed for complex proofs. It moves beyond basic one-step congruence problems, challenging students to synthesize multiple geometric concepts—including the Reflexive Property, Vertical Angles, and Segment Subtraction—into a coherent logical argument. Teachers can use this video to scaffold instruction for advanced proof writing or as a review tool for students struggling with multi-step logical deductions.