Interactive exercise. Assistance may be required. The second special right triangle that we will investigate is created from a square. Quilters and landscapers call this special right triangle a half-square triangle.

Let’s use a 45°-45°-90° triangle with a leg length of 1 unit to look for relationships among the lengths of the three sides of the triangle.

45, 45, 90 right triangle

Interactive exercise. Assistance may be required. Fold the right angle in half so that the two legs overlap.

Interactive exercise. Assistance may be required. Now, use the Pythagorean Theorem to find the length of the remaining side of your original triangle.

Interactive exercise. Assistance may be required. Fill in the chart like the one below to summarize your findings. You may make this chart in your notes.