# Two squares

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### 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,
H = square2.vertices,

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