An American High School Mathematics Examination Question

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

This Demonstration is an attempt to produce multiple-choice questions such as those posed on various examinations like the AHSME (American High School Mathematics Examination) and the AIME (American Invitational Mathematics Examination), or at the Australian mathematics competition and the European Mathematical Kangaroo. Here is a generalization of question 30 on the 1983 AHSME.

Contributed by: Izidor Hafner (April 2016)
Open content licensed under CC BY-NC-SA



Solution of problem 30: , [1, pp. 72].

In and , we have (in the order given) the condition angle-side-side. By the "ASS theorem", the angles and are either equal or supplementary. Since these triangles are not congruent (), we must have that and are supplementary. From we compute


Thus, and



[1] G. Berzsenyi and S. B. Maurer, eds., The Contest Problem Book V, Washington, DC: Mathematical Association of America, 1998.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.