[color=#000000]In the applet below, a quadrilateral is shown. [br]You can move the vertices of this quadrilateral wherever you'd like. [br][br]Interact with this applet for a few minutes, then answer the questions appear below it. [br]Be sure to change the locations of the quadrilateral's vertices each time [i]before[/i] and [i]after[/i] re-sliding the slider! [/color]

[color=#980000][b]Questions:[/b][/color][color=#000000][br][br]1) How do you know the [b]smaller white points[/b] are [b]midpoints[/b]? Explain. [br][br]2) Notice how the [b]midpoints of the sides[/b] of this quadrilateral form [b]vertices[/b] of yet [b]another quadrilateral[/b]. [br] How would you classify this [/color][color=#1e84cc][b]quadrilateral[/b][/color][color=#000000]? That is, what would be the [/color][color=#1e84cc][b]most specific name[/b][/color][color=#000000] you'd give [br] this [/color][color=#1e84cc][b]quadrilateral[/b][/color][color=#000000]? [br][br]3) What observation(s), in the applet above, prompted you to give the [/color][color=#1e84cc][b]classification[/b][/color][color=#000000] you did for (2)?[br] Explain fully why/how this applet informally suggests that your [/color][color=#1e84cc][b]answer to (2)[/b][/color][color=#000000] is correct. [br][br]4) Formally prove that the [b]midpoints of the sides[/b] of [i]any quadrilateral [/i]always form [b]vertices[/b][br] of this type of [/color][color=#1e84cc][b]specific quadrilateral[/b][/color][color=#000000]. Prove this using the format of a 2-column or paragraph proof. [br] (If you need a hint getting started, refer to [url=https://www.geogebra.org/m/NFCwzehu]this worksheet[/url].) [br][br]5) Use coordinate geometry to formally prove your response to (2) is true. [br] (Hint: Place one vertex of this quadrilateral at (0,0). Place another vertex at (2a, 0).) [/color]