Grade 6 | Unit 1 | Lesson 7: From Parallelograms to Triangles | Practice Problems

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.

Tags

CCSS.6.G.A.1

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.

• Yes, by joining them along one of the shorter sides.

• No, it cannot form a parallelogram that is not a square.

Tags

CCSS.1.G.A.2

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.

• 
• 
• C

• D

Tags

CCSS.1.G.A.1

CCSS.2.G.A.1

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.

Tags

CCSS.1.G.A.2

Tags

CCSS.6.G.A.1