Using Your Algebra Skills 9

Use a sheet of square dot paper and draw a square that is 1 by 1.

Draw in the diagonal. Use the Pythagorean Theorem to find the

length of the diagonal.

Did you say the diagonal was the ? 2

Use a sheet of square dot paper and draw a square that is 2 by 2.

Draw in the diagonal. Use the Pythagorean Theorem to find the

length of the diagonal.

8Did you say the diagonal was the ?

Remember that the diagonal inside a 1 x 1 square measures 2

How many of the orange diagonals fit on the green diagonal?

Another name for would be 8

2 2

Finding another name for 8

You might notice that 8 4 2

It follows that 4 2 4 2 2 2

Use a sheet of square dot paper and draw a square that is 3 by 3.

Draw in the diagonal. Use the Pythagorean Theorem to find the

length of the diagonal.

18Did you say the diagonal was the ?

Remember that the diagonal inside a 1 x 1 square measures 2

How many of the orange diagonals fit on the green diagonal?

Another name for would be

183 2

Finding another name for 18

Similarly 18 9 2 9 2 3 2

Use a sheet of square dot paper and draw a square that is 8 by 8.

Draw in the diagonal. Without using the Pythagorean Theorem

find the length of the diagonal.

How many segments fit on the diagonal of a 8 by 8 square?

2

8 2 64 2 64 2 128

Use a sheet of isometric dot paper and draw a an equilateral triangle that is 2 units on each side.

Draw in an altitude. Notice two right triangles

are formed. How long is each part of the base?

Use the Pythagorean Theorem to find the length of the altitude.

The altitude is 3

Use a sheet of isometric dot paper and draw a an equilateral triangle that is 4 units on each side.

Draw in an altitude. Notice two right triangles

are formed. How long is each part of the base?

Use the Pythagorean Theorem to find the length of the altitude.

Did you get the altitude to be ? 12

How many times does the red altitude fit on the green altitude?

Therefore, 12 2 3

Remember that the first altitude was . (Red Line)3

Use a sheet of isometric dot paper and draw a an equilateral triangle that is 6 units on each side.

Draw in an altitude. Notice two right triangles

are formed. How long is each part of the base?

Use the Pythagorean Theorem to find the length of the altitude.

Did you get the altitude to be ? 27

Draw in a large equilateral triangle whose side is an even number.

Find the length of all sides of the right triangle.

How many 3 ?

Use a sheet of isometric dot paper and draw a an equilateral triangle that is 4 units on each side.

Draw in an altitude. Notice two right triangles

are formed. How long is each part of the base?

Use the Pythagorean Theorem to find the length of the altitude.

Did you get the altitude to be ? 12

27 9 3 9 3 3 3

5 2 25 2 25 2 50

Study these equality statements to make some generalizations

What would be other names for each of the following?

3 2 4 5 5 9

54 12 72