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Warm-Up: Summary 1a + b bottom of page 8. AND Simplify: 8 2 Homework Answers 72 + 152 < 212 45-45-90 Special Triangle Discovery We begin with a square with 1 unit on each side. This is shown below. Find the measurement of all the angles and the lengths of each side. Add a diagonal to the above square. The diagonal creates two smaller triangles in your above square. Find the angle measures of the angles in the two triangles. Using the Pythagorean Theorem, find the length of the diagonal (or the hypotenuse of the right angle triangle). KEEP IN RADICAL FORM. We begin with a square with 2 unit on each side. This is shown below. Find the measurement of all the angles and the lengths of each side. Add a diagonal to the above square. The diagonal creates two smaller triangles in your above square. Find the angle measures of the angles in the two triangles. Using the Pythagorean Theorem, find the length of the diagonal (or the hypotenuse of the right angle triangle). KEEP IN RADICAL FORM. We begin with a square with 3 unit on each side. This is shown below. Find the measurement of all the angles and the lengths of each side. Add a diagonal to the above square. The diagonal creates two smaller triangles in your above square. Find the angle measures of the angles in the two triangles. Using the Pythagorean Theorem, find the length of the diagonal (or the hypotenuse of the right angle triangle). KEEP IN RADICAL FORM. Square with ___ Units 4 8 12 15 17 Side Length of a Leg Side Length of a Leg Side Length of Hypotenuse. Is there a pattern you notice? Explain it. Do you think this would work for all shapes (ie Rectangles, triangles etc.)? Explain why or why not. What effect does the size of the square have on the lengths of the sides? Conclusion: Given an “x” unit on each side square, what would be the lengths of the sides, and the length of the hypotenuse? Section 8.3 Notes: Special Right Triangles In a 45˚-45˚-90˚triangle, the legs 𝑙 are congruent and the hypotenuse, ℎ is 2 times the the length of a leg. 45˚-45˚90˚ Triangle *ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = 𝑙𝑒𝑔 ∙ 2 Theorem *ℎ = 𝑙 2 Example 1: Find the measure of each hypotenuse a. Example 1: Find the measure of each hypotenuse b. Example 1: Find the measure of each hypotenuse You can also work backwards using theorem 8.8 to find the legs of a 45° – 45° – 90° triangle a. Example 1: Find the measure of each hypotenuse You can also work backwards using theorem 8.8 to find the legs of a 45° – 45° – 90° triangle b. Example 2. The perimeter of a square is 48 meters. Find the length of a diagonal. Example 3. The perimeter of a square is 20 cm. Find the length of a diagonal. You Try! Find the value of x and y in each triangle. You Try! Find the value of x and y in each triangle. You Try! Find the perimeter of the given square. You Try!