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19.2 Pythagorean Theorem

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**A right triangle is a triangle that has a right (90 degree) angle**

A right triangle is a triangle that has a right (90 degree) angle. The 2 sides that form the right angle are called the legs of the triangle and the side opposite the right angle is called the hypotenuse. hypotenuse leg leg leg hypotenuse leg

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**The Pythagorean Theorem relates the sides of any right triangle**

The Pythagorean Theorem relates the sides of any right triangle. If a and b represent the legs and c the hypotenuse, then

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**Find the length of the hypotenuse:**

c 24 dm 10 dm

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**Find the length of the hypotenuse:**

8.00 cm 3.90 cm c

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**Find the length of the missing side**

b

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**Find the length of the missing side**

b

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**Use the Pythagorean theorem.**

How long must a guy wire be to reach from the top of a 15-m telephone pole to a point on the ground 10 m from the foot of the pole? Use the Pythagorean theorem. 10 m 15 m c

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**There are two special right triangles that we will further explore**

There are two special right triangles that we will further explore. They are called a 45, 45, 90 right triangle and a 30, 60 ,90 right triangle. The numbers refer to the measure of the angles in degrees.

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**The 45, 45, 90 triangle is an isosceles triangle which means the two legs have equal measure.**

hypotenuse Since the legs are equal, by the Pyth.Theorem, the hypotenuse has length = leg

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**Find the hypotenuse of an isosceles triangle that has equal sides of 2 m.**

? Hypotenuse has length =

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**If the hypotenuse of a 45, 45, 90 triangle is 5 cm long, how long is each leg.**

? 5 cm Since hyp = leg

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An equilateral triangle has 3 equal sides and 3 equal angles that each measures 60 degrees. The height bisects both the angle and opposite side making a 30, 60, 90 triangle. 30 ½ side or ½ hypot 60 60

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**Applying the Pythagorean Th**

Applying the Pythagorean Th. to this 30, 60, 90 triangles gives the following relations: 30 2x, side opposite right angle or longest side other leg 60 x, side opposite 30 or short leg

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**Find the missing measures.**

30 Hyp. = 2(short leg) = 2(7 in) = 14 in Other leg = short leg ? ? 60 7 in

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**Find the missing measures.**

60 ? Other leg = short leg ? 30 8 cm Hyp. = 2(short leg) = 2( 4.6in) = 9.2 in

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