From Parallelograms to Triangles

Aim: Decomposing Parallelograms into Triangles.

  • Draw a line to decompose each polygon into two identical triangles, if possible.  Use tool. If you choose to, you can also draw the triangles using the tool.

The height of the parallelogram on the right is 2 centimeters. How long is the base of that parallelogram? Explain your reasoning.

Aim: Decomposing parallelograms into Identical Triangles.

  • On the grid, draw at least three different quadrilaterals that can each be decomposed into two identical triangles with a single cut.​
  • Use the line tool to show the cut line.

Aim: Which triangles compose a parallelogram?

The applet below has eight pairs of identical triangles. You can check that out by clicking on “New Pair” to see the different triangles.

Move the triangles and arrange them to figure out which pair forms a parallelogram. Then answer the questions