Lesson 7: Practice Problems
Problem 1
To decompose a quadrilateral into two identical shapes, Clare drew a dashed line as shown in the diagram.
![A trapezoid with a height of 4 and bases of 6 and 2. It has a dotted line drawn from the end of the top base to the bottom.](../../../../../../embeds/5119bff1--6.1.C.PP_Image_5.1.png)
She said the that 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.
Problem 2
Triangle
![Two copies of a right triangle labeled R.](../../../../../../embeds/fdaccab9--6.1.C1.Image.09.R.png)
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 triangle. The left side of the triangle descends 2 units while moving left by 1 unit. The top side descends 1 unit while moving left 6 units. The bottom side moves up 1 unit while moving left 5 units.](../../../../../../embeds/b182e29f--6.1.C.PP.New.Image.02.png)
Problem 4
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 5 From Unit 1 Lesson 6
A parallelogram has a base of 9 units and a corresponding height of
units. What is its area? A parallelogram has a base of 9 units and an area of 12 square units. What is the corresponding height for that base?
A parallelogram has an area of 7 square units. If the height that corresponds to a base is
unit, what is the base?
Problem 6 From Unit 1 Lesson 5
Select all segments that could represent a corresponding height if the side
![A parallelogram with a bottom side labeled m and a right side labeled n. Dashed lines e, f, j, and k are drawn perpendicular to side m, and dashed lines g and h are drawn perpendicular to side n.](../../../../../../embeds/b4827c0f--6.1.B.PP.New.Image.10.png)
Segment
Segment
Segment
Segment
Segment
Segment
Segment
Segment