In this article, we offer a second proof of the triangle-in-a-triangle theorem, using the principles of similarity geometry. Then, using vectors, we prove a result which is a generalisation of that theorem.
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.
Every triangle has certain lines associated with it. The most prominent among them are the perpendicular bisectors of the sides, the bisectors of the angles, the altitudes, and the medians.
In Part I of this article we had showcased the triple (3, 4, 5) by highlighting some of its properties and some configurations where it occurred naturally. We now attempt to extend this to other triples of consecutive integers.

Hit the problems head on & solve them!

Use GeoGebra to check when will a rectangle have maximum area when it is inscribed in a triangle. 

In this article we examine how to prove a result obtained after careful GeoGebra experimentation. It was featured in the March 2015 issue of At Right Angles, in the ‘Tech Space’ section.
‘Low Floor High Ceiling’ activities are simple age-appropriate tasks which can be attempted by all the students in the classroom. The complexity of the tasks builds up as the activity proceeds so that each student is pushed to his or her maximum as they attempt their work. There is enough work for all, but as the level gets higher, fewer students are able to complete the tasks.

Find the area marked x.

In between 'This is not the first sentence of this article.' and 'This is the last sentence of the article. No this is. This.' Punya Mishra & Gaurav Bhatnagar invite you to the enchanting world of paradoxes which are literal, visual & of course in many cases mathematical. This is the concluding part on the said theme.


18085 registered users
6933 resources