Similar Triangles

Explain why (prove that) if lines AB, BC and CA are rotated through the same angle respectively around B, C and A as shown, then DEF is similar to ABC.

Please enable Java for an interactive construction (with Cinderella).

(1) Drag points A, B or C to change triangle ABC, or L to change the angle of rotation.

(2) Formulate a converse and investigate. If true, explain why (prove) or if false, give a counter-example.

(3) Investigate what happens if the same construction as in (1) is carried out with a quadrilateral, as well as consider its converse.

(Think about it before going to Quad)

Created by Michael de Villiers, 17 Nov 2007 with Cinderella