Shearing is a special affine transformation that preserves area, and is often useful in geometric problem solving and proving of theorems. Probably the most well-known example at high school level of a straightforward application of shearing is the theorem that two triangles with the same base and same height have the same area.

Below are some introductory examples of shearing, first in coordinate form, and then an example is given for an area ratio problem with regard to a parallelogram, and finally two simple proofs of the theorem of Pythagoras by using shearing. Use the Link buttons in the sketch to navigate to the relevant dynamic sketch.

An Area Preserving Transformation: Shearing

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Read up further about 'shearing' and other affine transformations like 'stretching', and their applications, and write a report.