Lesson 07: From Parallelograms to Triangles | Unit 1: Area and Surface Area

Open Ended

Clare drew a dashed line to decompose a quadrilateral into two shapes. She said that the two resulting shapes have the same area. Do you agree? Explain your reasoning.

Open Ended

Clare drew a dashed line to decompose a quadrilateral into two shapes. Did Clare partition the figure into two identical shapes? Explain your reasoning.

Open Ended

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.

Multiple Choice

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

Draw

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.

Multiple Choice

What type of quadrilateral is formed by the vertices (2,3), (5,3), (5,6), and (2,6) on the grid?

• Rectangle
• Parallelogram
• Trapezoid
• Rhombus

Draw

Draw an identical copy of each triangle such that the two copies together form a parallelogram. If you get stuck, consider using tracing paper.

Multiple Select

Andre drew a line connecting two opposite corners of a parallelogram. Select **all** true statements about the triangles created by the line that Andre drew.

• Each triangle has two sides that are 3 units long.

• Each triangle has a side that is the same length as the diagonal line.

• Each triangle has one side that is 3 units long.

• When one triangle is placed on top of the other and their sides are aligned, we will see that one triangle is larger than the other.

• The two triangles have the same area as each other.