Properties of a mathematical object undergoing a transformation that are unchanged by the transformation are called invariant. Manipulative 1 shows a dilation of a triangle. Properties of a triangle that are invariant under dilation are the measures of the angles, and the ratios between the measures of the sides. Properties of the triangle that are not invariant are the lengths of the sides and the area of the triangle.
Click on points and drag them to change the figure. Which of the following never change for dilation: Angle measure, length of side, ratio of sides, are of the triangle? |
Manipulative 1 - Invariant Created with GeoGebra. |
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