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8.1: Right Triangles Pythagorean Theorem Properties of Special Right Triangles.

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Presentation on theme: "8.1: Right Triangles Pythagorean Theorem Properties of Special Right Triangles."— Presentation transcript:

1 8.1: Right Triangles Pythagorean Theorem Properties of Special Right Triangles

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

3 Pythagorean Theorem Formula a 2 + b 2 = c 2 a and b represent the legs c represents the hypotenuse

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

5 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.

6 What is the length of the hypotenuse in the triangle below? a 2 + b 2 = c 2 2 4 h

7 Plug in the value for each variable in the formula. a 2 + b 2 = c 2 2 4 h 2 2 + 4 2 = h 2

8 What is the length of the hypotenuse in the triangle below? a 2 + b 2 = c 2 2 2 + 4 2 = h 2 4 + 16 = h 2 20 = h 2 2 4 h

9 What is the length of the hypotenuse in the triangle below? a 2 + b 2 = c 2 2 2 + 4 2 = h 2 4 + 16 = h 2 20 = h 2 2 4 h 20 = h 5 2

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

11 6 4 h a 2 + b 2 = c 2 4 2 + 6 2 = h 2 16 + 36 = h 2 52 = h 2 52 = h 7.21 = h 4 2 + 6 2 = h 2 16 + 36 = h 2 52 = h 2 52 = h 7.21 = h

12 What is the length of the missing leg in the triangle below? 3 x 5 a 2 + b 2 = c 2 Try this one...

13 Find the hypotenuse of the right triangle below? 5 3 x a 2 + b 2 = c 2 3 2 + x 2 = 5 2 9 + x 2 = 25 x 2 = 16 16x = x = 4 -9 - 9


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