Decomposing Two Congruent Two-Dimensional Figures into Parts with Equal Areas
T.I.P.S.
Students must be able to do three things with congruent two-dimensional figures:
• Break them into parts with equal areas
• Write the area of each part as a unit fraction of the whole figure
• Recognize that even though the parts have the same area, they do not have to be the same shape.
Example
Rectangle A is congruent to Rectangle B.
a) Draw segments in the rectangles that will divide the rectangles into shapes that have the equal areas, but are not the same exact shape. b) Explain how you know the areas are equal. c) Express the area of each part as a unit fraction of the whole rectangle.
Digital Tools
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3.6 Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional geometric figures to develop generalizations about their properties. The student is expected to:(E) decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole and recognize that equal shares of identical wholes need not have the same shape
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