Triangles, Squares and Unexpected Areas
Use the buttons in the app below to explore the construction step by step and find out an unexpected result!
Can you prove this property?
You can actually prove this result in different ways.
One way could be by using triangles metric properties, so trigonometry rules, but it involves a lot of calculations.
Here we will focus on the geometric properties of the objects and geometric transformations.
Use the slider in the app below and observe what happens.
Think about the formula you use to calculate the area of a triangle, and use the geometric objects that are congruent to the given ones after the transformation.
Inspired by an Nrich activity.