Summary We prove the next generalization of the Steiner-Lehmus theorem: if two equal cevians intersect with each other on the angle bisector of the third triangle vertex, then the triangle is ...

Constructions (accurate drawings) can be made using a ruler, a pair of compasses and a pencil. A line which cuts an angle into two equal side angles is called an angle bisector. In geometry a ...

In the diagram below, AB is the chord of a circle with centre O. OM is perpendicular to AB (meet at a right angle). Look at triangles OAM and OBM. The hypotenuses (OA and OB) are the same, as they are ...

They form a partially hinged dissection. Objects MA.304723.755, MA.304723.760, and MA.304723.804 form model 6TQ (angle bisectors of a triangle). A drawing for this model, dated April 23, 1932, is in ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

The secret to getting ahead is getting started. In the triangle above, segment BD is an angle bisector. Sides AB = 9x − 14, ...