A Math Forum Web Unit
Tom Scavo's

Right Triangles

Contents || Math Lessons

[Materials] [Length] [Area] [Pick's Theorem] [Dot Paper] [Epilogue]

[Lines] [Squares] [Rectangles] [Parallelograms] [Right Triangles] [Bibliography]

Find all right triangles

Objectives

• to continue developing the student's sense of area, especially the relation between the area of a right triangle and the area of the corresponding rectangle
• to associate certain attributes of right triangles with appropriate terminology (e.g., similar, isosceles)
• to review some geometric concepts (e.g., congruent, similar) in the context of parallelograms
• to experiment with geometric pattern making

Materials

• 5 x 5 geoboards (the kind that fit together to make a 10 x 10 geoboard) and rubber bands (various sizes and colors)
• at least five geoboards for the teacher and one for each student
• 5 x 5 geoboard dot paper (two or three sheets for each student)
• 10 x 10 geoboard dot paper (for extended activities)
• overhead projector; transparent geoboard or dot paper (with marking pens)

Warm-up activities

1. Make a rectangle on your geoboard. What is its area?
2. Make another right triangle on your geoboard and determine its area.
3. Find the right triangle with smallest area.
4. Find the right triangle with next smallest area.
5. Find the right triangle with largest area.
6. Find the right triangle with next largest area.

Main activity

Find all possible right triangles on a 5 x 5 geoboard. (There is a total of 17 right triangles.)

Homework

Order each of the right triangles found in the main activity by area. (In order, the 17 right triangles have area 1/2, 1, 1, 3/2, 2, 2, 2, 5/2, 3, 3, 4, 4, 9/2, 5, 5, 6, and 8 square units.)

Extended activities

1. Make an isosceles right triangle, namely, a right triangle having two equal sides

2. Make another isosceles right triangle, but with different area. Is this triangle similar to the first one?

3. Find another pair of isosceles right triangles (with different area).

4. Find four similar right triangles, all with different area.

5. Make a right triangle that is not isosceles.

6. Make two right triangles which are similar, but not isosceles.

7. Make a right triangle with area 1 square unit. Can you find another right triangle with area 1 square unit?

8. Find four right triangles with area less than 2 square units

9. There are three right triangles with area 2 square units. Can you find them?

10. Find a right triangle with area 2 1/2 square units.

11. Find a right triangle with area 3 square units. Can you find another right triangle with area 3 square units?

12. How many right triangles can you find with area 4 square units?

13. Find a right triangle with area 4 1/2 square units.

14. Find two right triangles with area 5 square units.

15. Continue this pattern of right triangles on a 10 x 10 geoboard and complete the table:

[Materials] [Length] [Area] [Pick's Theorem] [Dot Paper] [Epilogue]

[Lines] [Squares] [Rectangles] [Parallelograms] [Right Triangles] [Bibliography]