congruence

If two sides of a triangle have the same lengths as two sides of another triangle, and one angle of the first triangle has the same measure as one angle of the second triangle, what can be said about them? Under what circumstances will they be congruent to one another?

In this article, Shailesh Shirali begins with a seemingly simple question but develops the answer into not one, but four different proofs! While the content focuses on mathematics that has many applications, some of which are mentioned here, the multiplicity of proofs is an added draw, helping the teacher to illustrate innovative ways of thinking and connections across approaches.

In this episode of "How To Prove It" we study a number of possible characterizations of a parallelogram...

In this issue’s task we work with right-angled triangles, isosceles as well as scalene. The activity has enormous scope for creativity, visualisation, investigation, pattern recognition, documentation and conjecture. Facilitators should encourage students to come up with proofs for conjectures that they make.

The objective of this 'Low Floor High Ceiling' activity series is to challenge the problem-solving skills of students and in attempting them, each student is pushed to his or her maximum potential. There is enough work for all but as the level gets higher, fewer students are able to complete the tasks.
In this article, we return to Viviani's theorem and discuss a proof-without-words.
17587 registered users
6689 resources