JSXGraph
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Two squares
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<iframe 
    src="https://www.jsxgraph.uni-bayreuth.de/share/iframe/two-squares" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Two squares" 
    allowfullscreen
></iframe>
This code has to 
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>

<script type = "text/javascript"> 
    /*
    This example is licensed under a 
    Creative Commons Attribution ShareAlike 4.0 International License.
    https://creativecommons.org/licenses/by-sa/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID = 'board-0';

        var board = JXG.JSXGraph.initBoard(BOARDID, {
            boundingbox: [-4, 3, 4, -3],
            keepaspectratio: true
        });
    
        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]);
 </script> 
/*
This example is licensed under a 
Creative Commons Attribution ShareAlike 4.0 International License.
https://creativecommons.org/licenses/by-sa/4.0/

Please note you have to mention 
The Center of Mobile Learning with Digital Technology
in the credits.
*/

const BOARDID = 'your_div_id'; // Insert your id here!

    var board = JXG.JSXGraph.initBoard(BOARDID, {
        boundingbox: [-4, 3, 4, -3],
        keepaspectratio: true
    });

    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]);
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Two squares" description="This construction was copied from JSXGraph examples database: BTW HERE SHOULD BE A GENERATED LINKuseGlobalJS="false">
   /*
   This example is licensed under a 
   Creative Commons Attribution ShareAlike 4.0 International License.
   https://creativecommons.org/licenses/by-sa/4.0/
   
   Please note you have to mention 
   The Center of Mobile Learning with Digital Technology
   in the credits.
   */
   
       var board = JXG.JSXGraph.initBoard(BOARDID, {
           boundingbox: [-4, 3, 4, -3],
           keepaspectratio: true
       });
   
       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]);
</jsxgraph>

Two squares

Geometry
Consider two arbitrary squares *ABCD* and *BEFG* having the vertex *B* in common, see figure below. Prove that the straight lines *AG* and *CE* 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 HaĊĦek](//home.pf.jcu.cz/~hasek/)) 
// Define the id of your board in BOARDID

    var board = JXG.JSXGraph.initBoard(BOARDID, {
        boundingbox: [-4, 3, 4, -3],
        keepaspectratio: true
    });

    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]);

license

This example is licensed under a Creative Commons Attribution ShareAlike 4.0 International License.
Please note you have to mention The Center of Mobile Learning with Digital Technology in the credits.