Isosceles Right Triangle: Quick Investigation

Move any of the two large points (below) anywhere you'd like at any time. Slide the black slider to form an isosceles right triangle. Then, answer the questions that follow.

1.

Use the Angle tool to measure and display the measures of angles A and B. What is each angle measure?

2.

Suppose AB = 3 cm. Use the Pythagorean Theorem to determine the length of the hypotenuse of this isosceles right triangle in SIMPLE RADICAL FORM.

3.

Suppose AB = 4 cm. Use the Pythagorean Theorem to determine the length of the hypotenuse of this isosceles right triangle in SIMPLE RADICAL FORM.

4.

Suppose AB = 5 cm. Use the Pythagorean Theorem to determine the length of the hypotenuse of this isosceles right triangle in SIMPLE RADICAL FORM.

5.

Suppose AB = 6 cm. Use the Pythagorean Theorem to determine the length of the hypotenuse of this isosceles right triangle in SIMPLE RADICAL FORM.

6.

Do you notice anything interesting about your results from (2) - (5) above? If so, describe.

7.

In your own words, describe the relationship among the lengths of the legs and hypotenuse in any isosceles right triangle.