[size=150][color=#ff0000]Below are two [b]parallelogram [/b]templates. [br]In both templates,[b] move the points around to change the parallelogram's shape.[br][/b]As you move the points around, [b]look for what stays consistent. [br][/b]Then, answer each question below. [/color][/size]
[b]1) [/b]What is ALWAYS true in a parallelogram?
[b]2)[/b] Do you see any congruent triangles formed by the sides and diagonals in a parallelogram? If so, what are they, and which congruence theorem(s) (SSS, SAS, ASA, AAS) could be used to prove their congruence?
[size=150][b]Part II: Exploring Rhombus Properties[/b][color=#ff0000][br][br]Below are two [b]rhombus [/b]templates. [br]In both templates,[b] move the points around to change the rhombus' shape.[br][/b]As you move the points around, [/color][b][color=#ff0000]look for what stays consistent. [/color][br][/b][color=#ff0000]Then, answer each question below. [/color][/size]
[b]3) [/b]EFHG is constructed by following the steps below:[br]1) Construct a circle centered at point E. [br]2) Pick any two points on circle E. Label them point F and point H.[br]3) Construct a circle centered at point F, going through point E.[br]4) Construct a circle centered at point H, going through point E.[br]5) Find the point where circle F and circle H intersect. Label it as point G.[br]6) Connect E, F, G, and H to form a quadrilateral. [br][br][u]Definition of a rhombus:[/u] [i]a rhombus is an equilateral quadrilateral.[/i][br][br][b]Prove / explain:[/b] How does this construction process ensure that EFGH is a [b]rhombus[/b]? [br][i](It may help to move the points around and change the shape. Observe what relationships stays consistent, no matter where you move the points.)[/i]
[b]4) [/b]What is ALWAYS true in a rhombus?
[b]5) [/b]Do you see any congruent triangles formed by the sides and diagonals in a rhombus? If so, what are they, and which congruence theorem(s) (SSS, SAS, ASA, AAS) could be used to prove their congruence?[br][i](Hint: there are two sets of 2 and one set of 4)[/i]
[size=150][b]Part III: Exploring Rectangle Properties[/b][color=#ff0000][br][br]Below is a [b]rectangle [/b]template.[br][b]Move the points around to change the rectangle's shape.[br][/b]As you move the points around, [/color][b][color=#ff0000]look for what stays consistent. [/color][br][/b][color=#ff0000]Then, answer the question below. [/color][/size]
[b]6) [/b]What is ALWAYS true in a rectangle?
[b]7) [/b]Do you see any congruent triangles formed by the sides and diagonals in a rectangle? If so, what are they, and which congruence theorem(s) (SSS, SAS, ASA, AAS) could be used to prove their congruence?[br][i](Hint: there are 2 sets of 2 and 1 set of 4)[/i]
[size=150][b]Part IV: Exploring Kite Properties[/b][color=#ff0000][br][br]Below are two [b]kite [/b]templates.[br]In each template, [b]move the points around to change the kite's shape.[br][/b]As you move the points around, [/color][b][color=#ff0000]look for what stays consistent. [/color][br][/b][color=#ff0000]Then, answer the questions below. [/color][/size]
[b]8) [/b]What is ALWAYS true in a kite? [br]For context, the "main diagonal" in this example runs from W to Y.
[b]9) [/b]Do you see any congruent triangles formed by the sides and diagonals in a kite? If so, what are they, and which congruence theorem(s) (SSS, SAS, ASA, AAS) could be used to prove their congruence?[br][i](Hint: there are 3 sets of 2)[/i]
[size=150][b]Part V: Midsegments of Quadrilaterals[/b][color=#ff0000][br][br]Below is a template for any quadrilateral. [br]M, N, O, and P are constructed as the [b]midpoints [/b]of each side. [br][b]Move the points around to change the quadrilateral's shape.[br][/b]As you move the points around, [/color][b][color=#ff0000]look for what stays consistent. [/color][/b][/size]
[b]10) Make a conjecture: [/b]what kind of shape is [b][color=#0000ff]always [/color][/b]formed by the [color=#0000ff]midsegments [/color]of [color=#0000ff][b]any [/b]quadrilateral[/color]?
[b]11) Prove[/b] your conjecture.[br][i](Hint: look for triangles.)[/i]