Interesting problem on area and triangle.

In this article, we focus on investigations with graph paper. Pages 45 & 46 give guidelines for the facilitator, pages 43 & 44 are a worksheet for students. This time we explore quadrilaterals and triangles using lattice points.

An Angle-in-a- Quadrilateral Problem

A recent paper by Bizony (2017) discussed the interesting golden ratio properties of a Kepler triangle, defined as a right-angled triangle with its sides in geometric progression in the ratio 1 : √φ : φ, where φ =  (1 + √5)/2

A parallelogram may appear to be a very simple and basic shape of plane geometry, but its simplicity is deceptive; indeed it possesses a lot of richness of structure. Much of this richness is revealed when we ask the following question. What characterizes a parallelogram?

In this article, we study a few properties possessed by any quadrilateral whose diagonals are perpendicular to each other.

Here is an elegant and remarkably compact one-line proof for an inequality relating to the area of a quadrilateral.

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.
The situation of exactly three bisectors being concurrent is not possible. Or is it? The reader is invited to prove
this as well as observations regarding some of the special cases mentioned.


18339 registered users
7154 resources