parallelogram

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

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 an earlier issue of At Right Angles, we had studied a gem of Euclidean geometry called Napoleon's Theorem, a result discovered in post-revolution France. We had offered proofs of the theorem that were computational in nature, based on trigonometry and complex numbers. We continue our study of the theorem in this article, and offer proofs that are more geometric in nature; they make extremely effective use of the geometry of rotations

Here is a video by Rashmi Kathuria where she shows how one can make a parallelogram through paper folding. This video is taken from her YouTube channel.

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.

Problems ahead, solve them.

A simple hand pump can hand to explore interesting connections across concepts.

A nice investigation with dynamic geometry for students at high school is the so-called Midpoint Trapezium theorem...

This article describes how graph sheets can be used to introduce the concept of area to children. It demonstrates, with concrete examples, how the concept of area can be applied to certain geometrical figures, such as squares, rectangles, triangles or parallelogram.

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