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GeoGebra

Parallelogram Properties

Autor:mbader97, Rachel DellOrto
Below are two parallelogram templates. In both templates, move the points around to change the parallelogram's shape. As you move the points around, look for what stays consistent. Then, answer each question below.

1) What is ALWAYS true in a parallelogram?

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  • A
  • B
  • C
  • D
  • E
  • F
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2) 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?

Part II: Exploring Rhombus Properties Below are two rhombus templates. In both templates, move the points around to change the rhombus' shape. As you move the points around, look for what stays consistent. Then, answer each question below.

3) EFHG is constructed by following the steps below: 1) Construct a circle centered at point E. 2) Pick any two points on circle E. Label them point F and point H. 3) Construct a circle centered at point F, going through point E. 4) Construct a circle centered at point H, going through point E. 5) Find the point where circle F and circle H intersect. Label it as point G. 6) Connect E, F, G, and H to form a quadrilateral. Definition of a rhombus: a rhombus is an equilateral quadrilateral. Prove / explain: How does this construction process ensure that EFGH is a rhombus? (It may help to move the points around and change the shape. Observe what relationships stays consistent, no matter where you move the points.)

4) What is ALWAYS true in a rhombus?

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  • A
  • B
  • C
  • D
  • E
  • F
Antwort überprüfen (3)

5) 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? (Hint: there are two sets of 2 and one set of 4)

Part III: Exploring Rectangle Properties Below is a rectangle template. Move the points around to change the rectangle's shape. As you move the points around, look for what stays consistent. Then, answer the question below.

6) What is ALWAYS true in a rectangle?

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  • A
  • B
  • C
  • D
  • E
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7) 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? (Hint: there are 2 sets of 2 and 1 set of 4)

Part IV: Exploring Kite Properties Below are two kite templates. In each template, move the points around to change the kite's shape. As you move the points around, look for what stays consistent. Then, answer the questions below.

A kite is defined as a quadrilateral with two sets of congruent adjacent sides.

8) What is ALWAYS true in a kite? For context, the "main diagonal" in this example runs from W to Y.

Wähle alle richtigen Antworten aus
  • A
  • B
  • C
  • D
  • E
  • F
  • G
  • H
  • I
  • J
Antwort überprüfen (3)

9) 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? (Hint: there are 3 sets of 2)

Part V: Midsegments of Quadrilaterals Below is a template for any quadrilateral. M, N, O, and P are constructed as the midpoints of each side. Move the points around to change the quadrilateral's shape. As you move the points around, look for what stays consistent.

10) Make a conjecture: what kind of shape is always formed by the midsegments of any quadrilateral?

11) Prove your conjecture. (Hint: look for triangles.)

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