Decompose Quadrilaterals

To decompose a quadrilateral into two identical shapes, Clare drew a dashed line as shown in the diagram. Did Clare partition the figure into two identical shapes? Explain your reasoning.

Explain your reasoning.

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On the grid, draw at least three different quadrilaterals that can each be decomposed into two identical triangles with a single cut (show the cut line). One or more of the quadrilaterals should have non-right angles. Label the square with and S and the rectangle with and R.

To decompose a quadrilateral into two identical shapes, Clare drew a dashed line as shown in the diagram.

She said the that two resulting shapes have the same area. Do you agree? Explain your reasoning.

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Select all segments that could represent a corresponding height if the side n is the base.

• e

• f

• g

• h

• j

Is this hierarchy correct? 

• yes

• no

Quadrilateral that has two pairs of parallel sides

• Parallelogram

• Prism

• Polygon

• Triangle

On the grid, draw at least three different quadrilaterals that can each be decomposed into two identical triangles with a single cut (show the cut line). One or more of the quadrilaterals should have non-right angles. Identify the type of each quadrilateral.

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To decompose a quadrilateral into two identical shapes, Clare drew a dashed line as shown in the diagram. She said that the two resulting shapes have the same area. Do you agree? Explain your reasoning. Did Clare partition the figure into two identical shapes? Explain your reasoning.

• Yes, the resulting shapes are identical.

• No, the resulting shapes are not identical.

Solve for the area of this trapezoid.

Decompose it into other shapes.

• 56 units squared

• 112 units squared

• 420 units squared

• 70 units squared