PYTHAGOREAN THEOREAM
-
Upload
emil-nelson -
Category
Documents
-
view
213 -
download
1
Transcript of 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