8-6 and 8-7 Square Roots, Irrational Numbers, and Pythagorean Theorem.

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Presentation transcript:

8-6 and 8-7 Square Roots, Irrational Numbers, and Pythagorean Theorem

8-6 Square Roots and Irrational Numbers  Perfect Square – a number that is a square of an integer  Example: 4 is perfect square because of 2 2  9 is perfect square because of 3 2  Square root ( ) – is the opposite of squaring a number  irrational number – is number that cannot be written as a ratio (fraction) of two integers.  It does not terminate or repeat

8-6 Square Roots and Irrational Numbers

8-6 Square Roots and Irrational Numbers-ans About 4 About 2 About 6 About 7 About 9 8 ft

8-6 Square Roots and Irrational Numbers

8-6 Square Roots and Irrational Numbers-ans irrational rational

8-7 Pythagorean Theorem In a right triangle, the 2 shortest sides are the legs. The side opposite the right angle is the hypotenuse. The Pythagorean Theorem states that in any right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. a 2 + b 2 = c 2 You can find the length of the hypotenuse with the Pythagorean Theorem.

8-7 Pythagorean Theorem

8-7 Pythagorean Theorem-answers 18ft26 in

8-7 Pythagorean Theorem

8-7 Pythagorean Theorem-answers 9.4 m4.2 cm

8-7 Pythagorean Theorem

8-7 Pythagorean Theorem-answers 6.7 ft 24.1 cm

Review Area of Triangles and Trapezoids Area of Triangle – A = 1/2bh Area of Trapezoid – A = ½(b 1 + b 2 )h Remember that the base and height must make a right angle!!

Examples

Finding area using the Pythagorean Theorem To find the area of a triangle or trapezoid, you will need to find the missing side using the Pythagorean Theorem.

Finding area using the Pythagorean Theorem - answers To find the area of a triangle or trapezoid, you will need to find the missing side using the Pythagorean Theorem.

More triangle examples

More triangle examples - answers

Trapezoid Examples

Trapezoid Examples - answers

More examples

More examples - answers