Lesson 6: 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.

  1. She said the that two resulting shapes have the same area. Do you agree? Explain your reasoning.

  2. Did Clare partition the figure into two identical shapes? Explain your reasoning.

Problem 2

Triangle is a right triangle. Can we use two copies of Triangle to compose a parallelogram that is not a square?

Two copies of a right triangle labeled R.

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.
  1. parallelogram
  2. parallelogram
  3. parallelogram
  4. parallelogram

Problem 4

  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.

    blank grid

  2. Identify the type of each quadrilateral.

Problem 5

  1. A parallelogram has a base of 9 units and a corresponding height of units. What is its area?

  2. A parallelogram has a base of 9 units and an area of 12 square units. What is the corresponding height for that base?

  3. 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

Select all segments that could represent a corresponding height if the side is the base.

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.

  1. Segment

  2. Segment

  3. Segment

  4. Segment

  5. Segment

  6. Segment

  7. Segment

  8. Segment