WARM UP: What is the length of the hypotenuse of triangle RST? Cassie’s computer monitor is in the shape of a rectangle. The screen on the monitor is 11.5 in. high and 18.5 in. wide. What is the length of the diagonal? Round to the nearest tenth of an inch. A triangle has side lengths 24, 32, and 42. Is it a right triangle? Explain. A triangle has side lengths 9, 10, and 12. Is it acute, obtuse, or right? Explain. Can three segments with lengths 4 cm, 6 cm, and 11 cm be assessed to form an acute triangle, a right triangle, or an obtuse triangle? Explain.

8.2 - Special Right Triangles I CAN use the properties of 45 45 90 and 30 60 90 triangles.

Certain right triangles have properties that allow you to use shortcuts to determine side lengths without using the Pythagorean Theorem. 45 45 90 Triangle Theorem In a 45 45 90 triangle, both legs are congruent and the length of the hypotenuse is 2 times the length of a leg.

Problem: Finding the Length of the Hypotenuse What is the value of each variable?

Problem: Finding the Length of the Hypotenuse What is the length of the hypotenuse of a 45 45 90 triangle with leg length 5 3 ?

Problem: Finding the Length of the Hypotenuse What is the value of each variable?

Problem: Finding the length of a leg What is the value of x? 3 3 2 6 6 2

Problem: Finding the length of a leg The length of the hypotenuse of a 45 45 90 triangle is 10. What is the length of one leg?

Problem: Finding the length of a leg What is the value of x? 5 2 10 2 5 10

Problem: Finding Distance A high school softball diamond is a square. The distance from base to base is 60 ft. To the nearest foot, how far does a catcher throw the ball from home plate to second base?

Problem: Finding Distance You plan to build a path along one diagonal of a 100 ft.-by-100 ft. square garden. To the nearest foot, how long will the path be?

Problem: Finding Distance A courtyard is shaped like a square with 250-ft-long sides. What is the distance from one corner of the courtyard to the opposite corner? Round to the nearest tenth.

Another type of special right triangle is a 30 60 90 triangle. 30 60 90 Triangle Theorem In a 30 60 90 triangle, the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is 3 times the length of the shorter leg.

Problem: Using the Length of One Side What is the value of “d” in simplest radical form?

Problem: Using the Length of One Side What is the value of “f” in simplest radical form?

Problem: Using the Length of One Side What is the value of x?

Problem: Applying the 30 60 90 Triangle Theorem An artisan makes pendants in the shape of equilateral triangles. The height of each pendant is 18 mm. What is the length “s” of each side of a pendant to the nearest tenth of a millimeter?

Problem: Applying the 30-60-90 Triangle Theorem Suppose the sides of a pendant are 18 mm long. What is the height of the pendant to the nearest tenth of a millimeter?

Problem: Applying the 30-60-90 Triangle Theorem What is the height of an equilateral triangle with sides that are 12 cm long? Round to the nearest tenth.

After: lesson Check What is the value of x? If your answer is not an integer, express it in simplest radical form.

Homework: Page 503, #8 – 20 even, 21,22-26 even,29