1. Problem 6.3
Draw two triangles on a sheet of grid paper. Make sure the triangles are very different from one another.

2. Part A
Record the base, height, area, and perimeter of your triangle.

3. Part B Make a copy of your triangle, and cut out both copies.
Experiment with putting the two triangles together to make new polygons.
Describe and sketch the polygons that are possible.

4. Part C
Can you make a parallelogram by piecing together the two identical triangles?
If so, record the base , height, area, and perimeter of the parallelogram.
How do these measures compare to the measures of the original triangles?

5. Part D Draw a parallelogram on grid paper, and cut it out.
Can you cut the parallelogram into two triangles that are the same shape and size?
Describe and sketch what you find.

6. Summarize
Were you always able to make a parallelogram from two identical triangles?
What do two identical triangles and the parallelogram made from them have in common?
From your experimentation and what you already know about finding areas of parallelograms and rectangles, how can you find the area of a triangle without counting or estimating?

7. Follow-up
Use what you have learned to find the area and perimeter of this triangle.(see figure on follow-up on page 59.
What measurements do you need to find the perimeter in this triangle?
What are the edge lengths?
What is the perimeter of this triangle?

8. Follow-up
What measurements do you need to find the area of this triangle?
What are the base and height of this triangle?
How do you use these measurements to find the area of this triangle?

9. Follow-up
How can we test to see whether the answer is reasonable?