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Is there an averaging of center points here that we could find?

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Also interesting: this triangle doesn't have rotational symmetry but I think this might be the center. Are all 6 triangles equal area?

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Is there a center point to the trapezoid?

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How would we find the center point of a more organic or obscured shape?

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Using the equilateral triangle as a reference point and knowing that folding in the corners finds the center point, helped to conceptualize finding the center point for other shapes, such as the trapezoid or rhombus.

You can find the center point of some shapes two different ways. Specifically: Shapes that have an even number of equal sides and can also be built by equilateral triangles: rhombus.

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Figures without rotational symmetry (the trapezoid) are difficult to find the center. We believe there is one, but don't know how to find it.

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The center is a point where lines meet, depending on the shape it can be found by the intersection of diameters, diagonals,medians or lines of symmetry.

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Can you find the center of any shape if you inscribe them into a circle?

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The center point is the intersection of two or more lines of symetry. If a figure does not have two lines of symmetry - ??? (Like the trapezoid - we couldn't figure that one out!)

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We can inscribe a circle into a square and find the center from measuring and folding the square in half.

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The middle point where no matter where you cut the pizza, it will be equidistant (radius).

For other shapes that are not a circle, you can use the angle (corners) with equidistance folded in to find the middle point (center).

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The inside point that is equidistant from all edges of a circle.

The inside point that is equidistant from all vertices of a square.

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But, not all shapes can be inscribed in a circle?

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Rhombus vs Trapezoid - Monica and Elyssa

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Rhombus vs Trapezoid - Monica and Elyssa

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When you measure the center of the rhombus, you can find it by looking half way between the opposite vertices OR half way between the opposite sides. However, with the trapezoid, you can only find the center by looking at the halfway points for the opposite sides. If you measure the halfway points from opposite vertices, you don't get the center. Does center imply equivalency? The intersection in the middle of the trapezoid looks like the center but does not create equal pieces (while still LOOKING LIKE the center).

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If there is not multiple lines of symmetry, is there not a center?

Is it possible to have a center on shapes that have concave angles?

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What is the center?? - Monica and Elyssa

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What is the center?? - Monica and Elyssa

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If you use half the length and width to find the center, you get the bottom dot, which doesn't look like the center. If you use half the length from the vertex to the opposite side, you get the top dot, which looks more like the center, but it's not equidistant from the top and bottom. Why???

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We think that maybe not all shapes have a center, mostly with irregular shapes like a trapezoid or irregular triangles.

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The center of a circle is the point that is equidistant from any point on the circumference.

For triangles, squares and rectangles, and other shapes it is the point that equidistant from all corners.