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 ...

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 four triangular pieces of two models denoted by MA.304723.755 and MA.304723.760 may be arranged to form a parallelogram (in two ways) and a triangle (in two ways), constituting a partially hinged ...

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 ...

In maths, a construction is an accurate drawing. Besides constructing triangles, there are two main constructions which can be done using a ruler, a pair of compasses and a pencil: After the ...

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