Lesson 7
From Parallelograms to Triangles
Problem 1
To decompose a quadrilateral into two identical shapes, Clare drew a dashed line as shown in the diagram.

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She said the that two resulting shapes have the same area. Do you agree? Explain your reasoning.
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Did Clare partition the figure into two identical shapes? Explain your reasoning.
Solution
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Problem 2
Triangle R is a right triangle. Can we use two copies of Triangle R to compose a parallelogram that is not a square?

If so, explain how or sketch a solution. If not, explain why not.
Solution
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Problem 3
Two copies of this triangle are used to compose a parallelogram. Which parallelogram cannot be a result of the composition? If you get stuck, consider using tracing paper.


A
B
C
D
Solution
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Problem 4
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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.
- Identify the type of each quadrilateral.
Solution
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Problem 5
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A parallelogram has a base of 9 units and a corresponding height of \(\frac23\) units. What is its area?
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A parallelogram has a base of 9 units and an area of 12 square units. What is the corresponding height for that base?
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A parallelogram has an area of 7 square units. If the height that corresponds to a base is \(\frac14\) unit, what is the base?
Solution
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(From Unit 1, Lesson 6.)Problem 6
Select all the segments that could represent the height if side \(n\) is the base.

\(e\)
\(f\)
\(g\)
\(h\)
\(m\)
\(n\)
\(j\)
\(k\)
Solution
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(From Unit 1, Lesson 5.)