Here are two copies of a parallelogram. Each copy has one side labeled as the base and a segment drawn for its corresponding height and labeled . 

Two triangles, base b, height h. On right, b is slanted side and height is outside of triangle, perpendicular to the slanted side.

1. The base of the parallelogram on the left is 2.4 centimeters; its corresponding height is 1 centimeter. Find its area in square centimeters.
2. The height of the parallelogram on the right is 2 centimeters. How long is the base of that parallelogram? Explain your reasoning.

Two shapes are identical if they match up exactly when placed one on top of the other.

1. Draw one line to decompose each shape into two identical triangles, if possible. Use a straightedge to draw your line.

   

2. Which quadrilaterals can be decomposed into two identical triangles?

   Pause here for a small-group discussion.

3. Study the quadrilaterals that can, in fact, be decomposed into two identical triangles. What do you notice about them? Write a couple of observations about what these quadrilaterals have in common.

Your teacher will give your group several pairs of triangles. Each group member should take 1 or 2 pairs. 

1. 1. Which pair(s) of triangles do you have?

   2. Can each pair be composed into a rectangle? A parallelogram?

2. Discuss with your group your responses to the first question. Then, complete each statement with All, Some, or None. Sketch 1 or 2 examples to illustrate each completed statement.

   1. ________________ of these pairs of identical triangles can be composed into a rectangle.

   2. ________________ of these pairs of identical triangles can be composed into a parallelogram.