Shapes

Emma Shaw, Feb 16, 2021

Table of Contents

  1. 2D Shapes
    1. Could you fit it?
    2. Shape sorter
    3. Sort the geometric figures
    4. Regular Polygon Action!
    5. Angle Sum of a Triangle
    6. Classifying Quadrilaterals
  2. 3D Shapes
    1. 3D Shapes - Nets
    2. Which solid can be built from this net?
  3. Area
    1. Proof Without Words
  4. Proofs Without Words
    1. Proof Without Words
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    38. Proof Without Words
    39. Proof Without Words
    40. Pythagorean Theorem for Similar Shapes
    41. Proof Without Words
    42. Proof Without Words
    43. Proof Without Words
    44. Proof Without Words: Hunger's Law of Cosine Dissection
    45. Law of Cosines Proof Without Words
    46. Proof Without Words: 3-4-5 Right Triangle
    47. Loyd's Squares for a 3-4-5 Triangle
    48. Proof Without Words
    49. Da Vinci's Proof Without Words
    50. Mamikon's Proof Without Words
  5. Triangles
    1. Notice and Wonder
  6. Coordinates
    1. Part 1

1.

2D Shapes

  • 1. Could you fit it?
  • 2. Shape sorter
  • 3. Sort the geometric figures
  • 4. Regular Polygon Action!
  • 5. Angle Sum of a Triangle
  • 6. Classifying Quadrilaterals

1.1.

Could you fit it?

– Diego Lieban

1.2.

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2.

3D Shapes

  • 1. 3D Shapes - Nets
  • 2. Which solid can be built from this net?

2.1.

3D Shapes - Nets

Please watch this short video about how 3D shapes are made up of net shapes.
Please watch this short video about how 3D shapes are made up of net shapes.
Use the applet below to explore how nets form three dimensional shapes.
Exploring the properties of net shapes.
Begin by moving the red slider from left to right. Observe how the net forms the three dimensional shape of a cube. Move the red slider back to the left. Now begin changing the pattern of the net by moving the blue slider. Notice that though the pattern of the net changes, the different patterns still form a cube by moving the red slider from left to right.
Now use the following applet to explore how the net shape forms a cylinder.
And this net shape of a cone.
Classifying three-dimensional shapes.
There are three main elements that can be used when classifying three-dimensional shapes. These elements consist of faces, edges and vertices. Watch the following short video clip for an explanation of these three elements and how they are used to classify three-dimensional shapes.
Faces, edges and vertices: classifying three-dimensional shapes.
Faces of net shapes.
Which shape has the most circular faces?
Edges of three-dimensional shapes.
Which shape has the least number of edges.
Vertices of three-dimensional shapes.
Which of the shapes has the most number of vertices?
– Sam McClymont, Marty, Mathguru, Freyja Fallson-Ree, Sharyn, GeoGebra Materials Team, , Emma Shaw, levonatkinson

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3.

Area

  • 1. Proof Without Words

3.1.

Proof Without Words

Drag the points in the sketch below.[br]What do you notice? What does this prove? How does this prove it?
– Steve Phelps

4.

Proofs Without Words

Here is a GeoGebraBook of Proofs Without Words for the Pythagorean Theorem.

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  • 38. Proof Without Words
  • 39. Proof Without Words
  • 40. Pythagorean Theorem for Similar Shapes
  • 41. Proof Without Words
  • 42. Proof Without Words
  • 43. Proof Without Words
  • 44. Proof Without Words: Hunger's Law of Cosine Dissection
  • 45. Law of Cosines Proof Without Words
  • 46. Proof Without Words: 3-4-5 Right Triangle
  • 47. Loyd's Squares for a 3-4-5 Triangle
  • 48. Proof Without Words
  • 49. Da Vinci's Proof Without Words
  • 50. Mamikon's Proof Without Words

4.1.

– Steve Phelps

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5.

Triangles

  • 1. Notice and Wonder

5.1.

Notice and Wonder

When you slid the slider, what happened? Be precise![br]
What is this animation suggesting? How is this suggesting that?
– Steve Phelps

6.

Coordinates

  • 1. Part 1

6.1.

Part 1

Press the MOVE button below. Watch what happens. Then answer the question that follows.
Given [math]A=\left(1,2\right)[/math] and [math]B=\left(9,8\right)[/math],[br][br]How far did the runner travel EAST? [br]How far did the runner travel NORTH?
Now press the CONTINUE button in the app above. How far did the runner travel in the final part when moving from B to A? Show your work & reasoning below.
– Tim Brzezinski

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