Unit 1, Lesson 7
From Parallelograms to Triangles
Grade 6
Practice
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 that the 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.
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.
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
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.
Problem 6
Select all the segments that could represent the height if side \(n\) is the base.
\(e\)
\(f\)
\(g\)
\(h\)
\(m\)