Investigating 45-45-90 Triangles

WARM-UP

What type of triangle is provided in the figure if we were to describe it by its angles?

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What type of triangle is provided in the figure if we were to describe it by its sides?

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Find the missing side of the provided triangle and type your answer below. (Note: You can write on the figure above by using the Toolbar Image tool.)

Move any of the two large points (below) anywhere you'd like at any time. Then, answer the questions that follow.

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

How does this triangle and the triangle presented in the warm-up relate to each other? How do you know? (Hint: What theorem can we use?)

Suppose AB = 3 cm. Find the length of the hypotenuse of this isosceles right triangle in SIMPLE RADICAL FORM.

Suppose AB = 4 cm. Find the length of the hypotenuse of this isosceles right triangle in SIMPLE RADICAL FORM.

Suppose AB = 5 cm. Find the length of the hypotenuse of this isosceles right triangle in SIMPLE RADICAL FORM.

Do you notice anything interesting about your results from above? If so, describe.

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

Click on tool, then click the tool to write on the following modules. Write your work on the modules as you solve the problems below.

Enter the value you found for x below. Remember to provide your answer in simplest radical form.

Which method do you want to use to find the hypotenuse?

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