Quadrilaterals Investigation-2018
These applets are for you to use to identify any patterns/relationships you notice among the parts (sides, angles, diagonals, etc.) of various quadrilaterals.
Table of Contents
- Quadrilaterals/Parallelograms
- Quadrilateral Investigation
- Parallelograms Investigation
- Parallelogram (Scaffolded Discovery)
- Rhombuses
- Rhombus Action!
- Rhombus (Scaffolded Discovery)
- Rectangles
- Rectangle Action!
- Rectangle Diagonals
- Squares
- Square Action!
- Trapezoids
- Trapezoid Midsegment: 2 Discoveries
- Isosceles Trapezoid Action!
- Isosceles Trapezoid (Scaffolded Discovery)
- Kites
- Kite Action!
- Kite (Scaffolded Discovery)
- Midpoints (Bonus!)
- Quad Midpoints Action!
- Isosceles Trapezoid Midpoints
Quadrilateral Investigation
[color=#000000]In the applet below, quadrilateral [i]ABCD[/i] has been designed so that [/color][color=#6aa84f][b]angle [i]A[/i] and angle [i]C always [/i]remain congruent. [/b](In fact, you can adjust the measures of these angles using the slider in the top left corner.) [/color][b][color=#6aa84f][br][br][br][/color][color=#980000]Directions: [/color][color=#6aa84f][br][br][/color][/b][color=#000000]1) Move any of the [b]BIG POINTS[/b] around so that [/color][color=#cc0000][b]angle [i]B[/i] and angle [i]D[/i] become congruent.[/b][/color][color=#000000] [br][br]2) If this is the case, what special kind of quadrilateral do you have? [br][br]3) Use the tools of GeoGebra to prove your response to (2) is true. [br][br]4) Again, use the tools of GeoGebra to prove your response to (2) is true. [br] This time, use a manner different from the one you used in (3) above. [/color]
Rhombus Action!
[color=#000000]Slide the slider slowly in the applet below. Be sure to repeat this process a few times, making sure to change the locations of the rhombus's [/color][color=#ff00ff]3 pink vertices[/color] [color=#000000]each time before re-sliding the slider. [/color] [br][br][br][b][color=#0000ff]What properties, illustrated here, are [/color][color=#38761d]unique [i]only to rhombuses[/i][/color][color=#0000ff] and not to other parallelograms? [br][/color][/b][b][color=#0000ff]What properties, illustrated here, apply to all parallelograms? [/color][/b]
Rectangle Action!
[color=#000000]Slide the slider slowly in the applet below. Be sure to repeat this process a few times, making sure to change the locations of the rectangle's [/color][color=#ff00ff]3 pink vertices[/color] [color=#000000]each time before re-sliding the slider. [/color] [br][br][br][b][color=#0000ff]What properties, illustrated here, are [/color][color=#38761d]unique [i]only to rectangles[/i][/color][color=#0000ff] and not to other parallelograms? [br][br]Are there any other (older) theorems illustrated here? If so, describe.[/color][/b]
Square Action!
[color=#000000]Slide the slider slowly in the applet below. Be sure to repeat this process a few times, making sure to change the locations of the [/color][color=#ff00ff]pink points[/color] [color=#000000]each time before re-sliding the slider. [/color] [br][br][br][b][color=#0000ff]What properties, illustrated here, are [/color][color=#38761d]unique [i]only to squares[/i][/color][color=#0000ff] and not to other parallelograms? [br][/color][/b][b][color=#0000ff]What properties, illustrated here, also apply to rhombuses? [br][/color][/b][b][color=#0000ff]What properties, illustrated here, also apply to rectangles?[br][/color][/b][b][color=#0000ff]What properties, illustrated here, apply in general to [i]all parallelograms[/i]? [/color][/b][b][color=#0000ff] [br][br][/color][/b]What is the measure of each gray angle? Explain how you know this to be true. [color=#0000ff][br][/color][color=#ff00ff]What is the measure of each pink angle? Explain how you know this to be true. [/color]
Trapezoid Midsegment: 2 Discoveries
[color=#000000]A [/color][b][color=#000000]MIDSEGMENT of a [/color][color=#ff00ff]trapezoid[/color][/b][color=#000000] is a [b]segment that connects the midpoints of its 2 non-base sides (legs)[/b]. [/color][br][br][color=#000000]Interact with the applet below for a few minutes. [br][b]Be sure to change the locations of the trapezoid's VERTICES lots of times![/b][/color][br][br][b][color=#980000]What 2 conclusions can you make about the median of any trapezoid? [/color][/b][color=#000000] [/color]
[b][color=#980000]Construct a valid 2-column, paragraph, or coordinate geometry proof to prove each conclusion true. [/color][/b]
Kite Action!
[color=#1e84cc][i]Note: This applet works best if the kite is kept convex. [/i][/color][color=#000000][br][br]Interact with the applet below for a few minutes[/color][color=#000000] to identify any patterns/relationships you[br]notice among the parts (sides, angles, diagonals, etc.) of a kite. [/color]
Quad Midpoints Action!
[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 to identify any patterns/relationships you[br]notice among the parts (sides, angles, diagonals, midpoints, etc.) of a quadrilateral. [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]