Right Triangles

Contents || Math Lessons

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

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

## 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 a10 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

- Make a rectangle on your geoboard. What is its area?
- Make another right triangle on your geoboard and determine its area.
- Find the right triangle with smallest area.
- Find the right triangle with next smallest area.
- Find the right triangle with largest area.
- 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

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

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

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

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

- Make a right triangle that is not isosceles.

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

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

- Find four right triangles with area less than 2 square units

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

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

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

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

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

- Find two right triangles with area 5 square units.

- 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]

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