PYTHAGOREAN THEOREAM

PYTHAGOREAN THEOREAM

• http://www.youtube.com/watch?v=uaj0XcLtN5c

http://www.youtube.com/watch?feature=player_detailpage&v=DRRVu-RHQWE

What is the relationship among the lengths of the sides of a right triangle

http://www.youtube.com/watch?v=uaj0XcLtN5c

Calculating this becomes:

9 + 16 = 25

WIKIPEDIACCSC Alignnment: 8.G.B.6

Pythagoras applied to similar triangles

Pythagoras by pentagons

Trig Functions

One of the best known mathematical formulas is Pythagorean Theorem, which provides us with the relationship between the sides in a right triangle. A right triangle consists of two legs and a hypotenuse. The two legs meet at a 90° angle and the hypotenuse is the longest side of the right triangle and is the side opposite the right angle.

Write it down as an equation:

abc triangle a^2 + b^2 = c^2

The Pythagorean Theorem tells us the relationship in every right triangle

a^2+b^2=c^2

Example:

Example: Does this triangle have a Right

Angle?

10 24 26 triangle

Does a^2 + b^2 = c^2 ?

C^2 = 10^2+24^2 = 676

They are equal, so ...

Yes, it does have a Right Angle!

Let's check if the areas are the same:

3^2 + 4^2 = 5^2

Calculating this becomes:

9 + 16 = 25

It works ... like Magic!

• Example: Solve this triangle.• A^2 + b^2 = c^2

• 5^2 + 12^2 = c^2• 25 + 144 = c2• 169 = c2• C^2 = 169• c = √169• c = 13

example: Does this triangle have a Right Angle?• Triangle with roots

3 + 5 = 8 ? Yes, it does!So this is a right-angled triangle

(√3)^2 + (√5)^2 = (√8)^2 ?

Leg^2 + leg^2 = hypotenuse ^2

You Can Prove The Theorem Yourself !

proof of the Pythagorean Theorem and it converse: In any right triangle, the sum of the squares of the legs equals the square of the hypotenuse (leg2 + leg2 = hypotenuse2). The figure below shows the parts of a right triangle.

Leg^2 + leg^2 = hypotenuse^2

hypotenuse2 – leg2 = leg2

proof• 3^2 + 4^2 = x^2

26^2 – 24^2 =x^2 • 9 + 16 = x^2

676 – 576=x^2• √25 = √x^2

√100 = √x^2

10 = x • √25 = x • 5 = x

distance formula: The distance d between the points A = (x1, y1) and B = (x2, y2) is given by the formula:

The distance formula can be obtained by creating a triangle and using the Pythagorean Theorem to find the length of the hypotenuse. The hypotenuse of

the triangle will be the distance between the two points.

√

distance formula

For example, consider the two points A (1,4) and B (4,0),

so: x1 = 1, y1 = 4, x2 = 4, and y2 = 0.

Substituting into the distance formula we have:

Sides relationships

PRACTICAL APPLICATION

SOH, CAH, TOA

The Pythagorean theorem

Right Angle Trignometry