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6.3 Investigating Connections between Measurements and Scale Factors of Similar Figures

Grade:
6-8
Standards:
Geometry
Math Content:
Geometry

To interchange between the 2D and 3D mode, click on the tabs, found on the upper right hand corner of the interactive.

There are three shapes to explore in each mode. Use the scale factor slider to change the size of the purple shape in relation to the red one.

In the 2D mode, the dimensions of the red shape can we changed by clicking a dragging a green vertex.
In both modes, graphs and measures can be observed on the right panel by clicking on the tabs.

  • How are the perimeters, areas, and side lengths of similar rectangles related? Change the size and shape of the purple rectangle. Notice that the purple and red rectangles are and remain similar (congruent angles, proportional sides). Observe the changes in the measurements.
  • Investigate how changing the lengths of the sides of a rectangular prism affects the volume and surface area of the prism. First notice start with two congruent rectangular prisms (equal angles and equal sides). Now change the size of the purple prism. Are the two prisms still congruent? Are they similar? Look at the volume, and observe the changes in the measurements. What is being depicted in the graph? What can you say about the relationship between the side lengths and the volume of a rectangular prism?
  • Do the same for the surface area. What is being depicted in the graph? What can you say about the relationship between the side lengths and the surface area of a rectangular prism?