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Math · Ages 6–8 · 15 minutes

Build a Rectangle from Two Triangles

Use a diagonal cut to explore how two triangles can make a rectangle.

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Build a Rectangle from Two Triangles

Name:                              
Date:              

Today I am practising: decomposing and recomposing a rectangle along a diagonal

1

Draw a rectangle on scrap paper. Mark two opposite corners.

2

Connect those corners with a straight diagonal.

3

Count the sides of each part. What shapes are the parts?

4

With adult help, cut on the diagonal and separate the parts.

5

Put the parts together to restore the rectangle. Describe which edges meet.

6

Explain why a diagonal makes two triangles even when the rectangle is long and narrow.

Grown-up guide
  1. Use a rectangle large enough to cut and handle.
  2. Avoid making a crease through side midpoints instead of opposite corners.
  3. Ask the learner to trace the boundary of each part before naming it.