Pythagorean Theorem Properties of Special Right Triangles

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Presentation transcript:

Pythagorean Theorem Properties of Special Right Triangles

What is the Pythagorean Theorem used for? to find the length of a missing side in a right triangle n 5 4

Pythagorean Theorem Formula a and b represent the legs a2 + b2= c2 c represents the hypotenuse a and b represent the legs

Always opposite of the 90 degree angle Where is it located??? c Leg a Hypotenuse Always opposite of the 90 degree angle b Leg

Remember!!! The Pythagorean Theorem can ONLY be used on Right Triangles. The Legs are ALWAYS the sides ADJACENT (next to) the 90 degree angle. C is ALWAYS the Hypotenuse (the slant). The Hypotenuse is ALWAYS opposite the 90 degree angle.

What is the length of the hypotenuse in the triangle below? a2 + b2= c2 2 4 h

Plug in the value for each variable in the formula. a2 + b2= c2 22 + 42= h2 2 4 h

What is the length of the hypotenuse in the triangle below? 2 4 h a2 + b2 = c2 22 + 42 = h2 4 + 16 = h2 20 = h2

What is the length of the hypotenuse in the triangle below? a2 + b2 = c2 2 4 h 22 + 42 = h2 4 + 16 = h2 20 = h2 = h 20 = h 2 5

Try this one . . . Find the hypotenuse of the right triangle below? 4 6 h

Find the hypotenuse of the right triangle below? a2 + b2 = c2 42 + 62 = h2 16 + 36 = h2 52 = h2 52 = h 7.21 = h 42 + 62 = h2 16 + 36 = h2 52 = h2 52 = h 7.21 = h 4 6 h

Try this one . . . What is the length of the missing leg in the triangle below? 5 3 a2 + b2 = c2 x

Find the hypotenuse of the right triangle below? a2 + b2 = c2 32 + x2 = 52 5 3 9 + x2 = 25 -9 - 9 x x2 = 16 x = 16 x = 4