Example — understanding a geometry problem

Example — Understanding a geometry problem

“In an isosceles triangle the bisector of the apex angle is also an altitude and a median. Prove it.”

• Data: triangle $ABC$ with $AB\cong AC$ (isosceles), bisector $AM$ of the angle $\widehat{A}$, with $M\in BC$.
• Thesis (the “unknown”): two things, not one — $AM\perp BC$ and $BM\cong MC$.
• Drawing: an isosceles triangle with base $BC$ and segment $AM$ starting from $A$ and touching $BC$; on the figure one immediately marks the information already known (the two equal sides with a tick, the angle at $A$ divided in half by the bisector).

Only now that everything is “on the sheet” does it make sense to start reasoning.

Links

Topics: Working method
Concepts: Data and unknowns · Problem solving
Skills: Proving · Synthetic geometry