Polygon Decomposition Practice

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Date:

📐 Part 1: Identifying Decomposed Polygons

1. A pentagon was cut into two parts: a triangle and a quadrilateral. Which statement is correct?

The parts have more sides than the original pentagon

The parts have fewer sides than the original pentagon

The parts have the same number of sides as the original pentagon

2. When you decompose a hexagon into smaller polygons, which shapes could you make? (Check all that apply)

Triangles

Rectangles

Circles

Quadrilaterals

3. If you cut a rectangle with one straight line, what two shapes will you always get?

Two triangles

Two rectangles

A triangle and a rectangle

Two quadrilaterals

4. What does it mean to "decompose" a polygon?

To draw it larger

To break it into smaller polygons

To count its sides

To color it in

5. Draw a line in the rectangle below to decompose it into two triangles.

6. Draw lines in the pentagon below to decompose it into a triangle and a quadrilateral.

7. Look at your decomposition in question 6. Name the two polygons you created:

Polygon 1: __________________ Polygon 2: __________________

8. Explain how you would decompose a hexagon into three triangles. Use words like "draw lines," "connect," and "vertices" in your explanation.

9. A student says: "I can cut any polygon into only squares." Do you agree or disagree? Explain your reasoning.

10. Challenge: How many different ways can you decompose a quadrilateral into two triangles? Draw your answer and explain.