Matter of Scale
This problem uses enlargements, scale factors and similar triangles to create a proof of Pythagoras' theorem.
This problem can be used alongside other proofs of Pythagoras' theorem, and students can consider which ones they think are most convincing, and which are easiest to understand/explain.
Students can also investigate a proof of the Converse of Pythagoras.
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Some(?) of the Parts
A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle
Ladder and Cube
A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?
At a Glance
The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?