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How can shapes be partitioned into equal areas?
Goal:
Goal:
Think About It!
Goal: Discover ways to partition shapes into equal areas.
Daniel started his drawing by making a line of symmetry. A line of symmetry is a line that a shape can be folded over so that both sides are identical.
When he drew that line, he created 2 identical rectangles. He drew 2 more lines of symmetry down the middle of each new rectangle. This partitioned the rectangle into 4 equal parts, all the parts are the same. To partition something means to divide something into equal parts.
Let's look at how lines of symmetry can partition shapes into equal parts. Click through the tabs below
Rectangles
Rectangles have a total of 2 lines of symmetry. Click on each picture below to see how rectangles can be partitioned.
One line of symmetry
One line of symmetry partitions the rectangle into 2 equal parts.
Two lines of symmetry
Two lines of symmetry partition the rectangle into 4 equal parts.
Squares
Squares have 4 total lines of symmetry. Click on each square to see it partitioned into different equal parts.
One line of symmetry
One line of symmetry partitions the square into 2 equal parts.
Two lines of symmetry
Two lines of symmetry partition the square into 4 equal parts.
Four lines of symmetry
Four lines of symmetry partition the square into 8 equal parts.
Circles
Circles have as many lines of symmetry as you need. Let’s look at a few examples of how circles can be partitioned. Click on each circle to see an example of how it can be partitioned.
One line of symmetry
One line of symmetry partitions the circle into 2 equal parts.
Three lines of symmetry
Three lines of symmetry partition the circle into 6 equal parts.
Five lines of symmetry
Five lines of symmetry partition the circle into 10 equal parts.
Equal Parts
When shapes are partitioned into equal parts, they can represent fractions. Each part represents 1 part out of the total shape. So, we write 1 as the numerator (the number on the top of the fraction). The denominator (the number on the bottom of the fraction) is the total number of equal parts that make up the shape. Click on each partitioned shape to see its fractional parts.
Two lines of symmetry partition the rectangle into 4 equal parts.
Each equal part represents \(\Large\frac{1}{4}\) of the rectangle.
Four lines of symmetry partition the square into 8 equal parts.
Each equal part represents \(\Large\frac{1}{8}\) of the square.
Three lines of symmetry partition the circle into 6 equal parts.
Each equal part represents \(\Large\frac{1}{6}\) of the circle.