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RIGHT TRIANGLES A RIGHT TRIANGLE is a triangle with one right angle. a b c Sides a and b are called legs. Side c is called the hypotenuse.

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Presentation on theme: "RIGHT TRIANGLES A RIGHT TRIANGLE is a triangle with one right angle. a b c Sides a and b are called legs. Side c is called the hypotenuse."— Presentation transcript:

1 RIGHT TRIANGLES A RIGHT TRIANGLE is a triangle with one right angle. a b c Sides a and b are called legs. Side c is called the hypotenuse.

2 RIGHT TRIANGLES A RIGHT TRIANGLE is a triangle with one right angle. a b c The legs are the sides of the right angle.

3 RIGHT TRIANGLES A RIGHT TRIANGLE is a triangle with one right angle. a b c The hypotenuse is the side opposite the right angle. The hypotenuse is always the longest side of a right triangle.

4 PYTHAGOREAN’S THEOREM If a and b are the lengths of the sides of a right triangle, and c is the length of the hypotenuse, then the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. a b c a 2 + b 2 = c 2

5 PYTHAGOREAN’S THEOREM 3 4 c a 2 + b 2 = c 2 3 2 + 4 2 = c 2 9 + 16 = c 2 25 = c 2 c = 5 Find the length of the hypotenuse.

6 PYTHAGOREAN’S THEOREM a 6 9 a 2 + b 2 = c 2 a 2 + 6 2 = 9 2 a 2 + 36 = 81 a 2 = 45 Find the length of the missing side. a =

7 PYTHAGOREAN’S THEOREM 6 5 8 a 2 + b 2 = c 2 5 2 + 6 2 = 8 2 25 + 36 = 64 Not True A triangle has sides of 5, 6, and 8. Is it a right triangle? No. It is not a right triangle.

8 PYTHAGOREAN’S THEOREM 30’ 15’ x a 2 + b 2 = c 2 30 2 + 15 2 = x 2 x 2 = 1125 A telephone pole is 35’ tall. How long is the guy wire if it is attached 5’ below the top of the pole and 15’ from the base of the pole? (nearest hundredth) x = 33.54 ft.

9 THE DISTANCE FORMULA Given two points, (x 1, y 1 ) & (x 2, y 2 ), the distance between the points may be found using the formula:

10 THE DISTANCE FORMULA Find the distance between (5, 3) & (-2, 1)

11 THE DISTANCE FORMULA Find the distance between (5, -3) & (5, 7)

12 FLASH CARDS Mid-Chapter Review Simplify:

13 FLASH CARDS Mid-Chapter Review Simplify:

14 FLASH CARDS Mid-Chapter Review Simplify:

15 FLASH CARDS Mid-Chapter Review Simplify:

16 FLASH CARDS Mid-Chapter Review Simplify:

17 FLASH CARDS Mid-Chapter Review What is the conjugate of ?

18 FLASH CARDS Mid-Chapter Review Simplify:

19 FLASH CARDS Mid-Chapter Review Solve:

20 FLASH CARDS Mid-Chapter Review Solve:

21 FLASH CARDS Mid-Chapter Review x 3 6 Solve for x

22 FLASH CARDS Mid-Chapter Review Find the distance between (8, -2) and (-3, -2).

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