10/15/ : Special Right Triangles1 G1.2.4: Prove and use the relationships among the side lengths and the angles of 30°- 60°- 90° triangles and 45°- 45°- 90° triangles. L1.1.6: Explain the importance of the irrational numbers √2 and √3 in basic right triangle trigonometry, the importance of π because of its role in circle relationships, and the role of e in applications such as continuously compounded interest.

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Daily Quiz 5/5/2011 Determine the perimeter of the triangle below.

10/15/ : Special Right Triangles4 Isosceles Right Triangles If a right triangle is isosceles, then it has 2 ___________ _________ and 2 ___________ __________. This means the measure of each acute angle must be ______. Thus another way to refer to Isosceles Right Triangles is as ___________ right triangles.

Isosceles Right Triangle Theorem If each leg of an isosceles right triangle is x units long, then the hypotenuse is xtimes the square root of 2 units long.

10/15/ : Special Right Triangles Right Triangles

10/15/ : Special Right Triangles7 The triangle below is an isosceles right triangle. What is the length of the hypotenuse? Calculate your answer 2 different ways. 6

DQ 5/6/2011 An isosceles triangle has perimeter of feet. What is the length of the hypotenuse of the triangle?

10/15/ : Special Right Triangles13 If one leg of an isosceles right triangle measures 15 feet, what is the perimeter of the triangle?

10/15/ : Special Right Triangles14 What is the perimeter of the square? Class work – 2pts 2 minutes

In an isosceles right triangle, the hypotenuse is 12. What is the length of one (1) of the sides? A. B. C. D. E. Class work – 2pts 3 minutes

10/15/ : Special Right Triangles16 The largest triangle is equilateral and the segment in the interior is perpendicular to the base. Determine the values of x and y. 10 x y

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10/15/ : Special Right Triangles Right Triangles When we cut an equilateral triangle with one altitude, we form 2 congruent right triangles each with one 30 and one 60 degree angle. These are called right triangles.

10/15/ : Special Right Triangles Right Triangle Theorem If the shortest leg of a right triangle is x units long, then the hypotenuse is 2x units long and the longer leg is x times the square root of 3 units long.

30 – 60 – 90 Triangle 60° 30° x 2xx√3

10/15/ : Special Right Triangles21 Solve for x and y 60  18 x y

10/15/ : Special Right Triangles22 Solve for x and y 60° y x 24

10/15/ : Special Right Triangles23 Solve for x and y 60° y x

10/15/ : Special Right Triangles 24 An altitude of an equilateral triangle is 8.3 meters. Find the perimeter of the triangle to the nearest tenth of a meter.

10/15/ : Special Right Triangles25 Assignment Pages , # (odds), 33