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Warm-up Find the missing length of the right triangle if a and b are the lengths of the legs and c is the length of the hypotenuse. a = b = a = 2.

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Presentation on theme: "Warm-up Find the missing length of the right triangle if a and b are the lengths of the legs and c is the length of the hypotenuse. a = b = a = 2."— Presentation transcript:

1 Warm-up Find the missing length of the right triangle if a and b are the lengths of the legs and c is the length of the hypotenuse. a = b = a = c = 3. a = b = c = 3 b = 2 c =

2 If we represent the legs of an isosceles right triangle by 1, we can use the Pythagorean Theorem to establish relationships between the lengths of the legs and the hypotenuse.  These "special" formulas allow us to quickly arrive at answers regarding the lengths of sides in this triangle. There are two "special" formulas that apply ONLY to the 45º-45º-90º triangle.

3 45º-45º-90º (Isosceles Right Triangle) "Special" Formulas

4 If you draw an altitude in an equilateral triangle, you will form two congruent 30º-60º-90º triangles.  With the help of the Pythagorean Theorem, we can establish "special" relationships between the sides of a 30º-60º-90º triangle.  These relationships form "short cut formulas" that will allow us to quickly arrive at answers regarding side lengths. There are three "special" formulas that we can establish that apply ONLY to the 30º-60º-90º triangle.

5 30º-60º-90º "Special" Formulas
Labeling: H = hypotenuse LL = long leg (across from 60º) SL = short leg (across from 30º)

6 30º-60º-90º "Special" Formulas
Short Cut Formulas: You must remember that these formulas can be used ONLY in a 30º-60º-90º triangle.

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