[color=#000000]Creation of this applet was initially inspired by a Twitter conversation among [url=https://twitter.com/MrHonner]Patrick Honner[/url], [url=https://twitter.com/misterwootube]Eddie Woo[/url], [url=https://twitter.com/EulersNephew]Chris Bolognese[/url], and [url=https://twitter.com/stevenstrogatz]Steven Strogatz[/url]. Here's the [url=https://twitter.com/MrHonner/status/762796821756387328]Twitter link[/url]. It is a revamped version of this [url=https://www.geogebra.org/m/vusfNP5g]previously created GeoGebra resource[/url]. [br][br][br]Before playing with the applet below, recall the theorem you've already discovered and proven in class and also illustrated here on [url=https://www.geogebra.org/m/uNW647XY]this animation[/url]. (For a quick, informal investigation of this theorem, refer [url=https://www.geogebra.org/m/xGxYdjWX]here[/url].) [br]Notice how on either resource, all 4 vertices of the original quadrilateral were coplanar. [br][/color][i][color=#ff7700]But what happens when we have 4 non-coplanar points?[/color][/i][color=#000000] Check it out below: [br][/color] [br]Feel free to move the [b][color=#ff7700]ORANGE VERTICES[/color] [/b]of this original "quadrilateral" anywhere you'd like! [br][br]How can we formally prove what is dynamically illustrated here? [br][br][b][color=#1e84cc]To explore in Augmented Reality, see the directions below the applet. [/color][/b]

1) Open up GeoGebra 3D app on your device. [br][br]4) Go to the MENU (horizontal bars) in the upper left corner. Select OPEN. [br] In the Search GeoGebra Resources input box, type [b]fvjqryvg[/b][br] (Note this is the resource ID = last 8 digits of the URL for this resource.)[br][br]5) In the resource that uploads, zoom in/out if needed.[br][br]The slider you see controls the animation. You can also move the 4 large points around at any time.