Two squares

Example: Two squares

Consider two arbitrary squares ABCD and BFGE having the vertex B in common, see figure below. Prove that the straight lines AE and CF are perpendicular for each such two squares.

(Source: Maria Alessandra Mariotti: Reasoning, proof and proving in mathematics education. Proceedings of the 10th International Congress on Mathematical Education (ICME), 4-11 July, 2004. 2008. Construction by Roman Hašek)

The JavaScript code

(function() {
    var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-4, 3, 4, -3]});

    var A = board.create('point', [-3, -1], {color: 'blue'}),
        B = board.create('point', [0, -1], {color: 'blue'}),
        E = board.create('point', [1, -2], {name: 'E', color: 'blue'}),

        square1 = board.create('regularpolygon', [A, B, 4], {name: 'Square 1'}),
        square2 = board.create('regularpolygon', [B, E, 4], {name: 'Square 2'}),

        C = square1.vertices[2],
        H = square2.vertices[3],

        p = board.create('line', [A, H]),
	q = board.create('line', [E, C]);
})();