Presentation is loading. Please wait.

Presentation is loading. Please wait.

6/22/20161 2 Types of Triangles  Types by Length Equilateral Isosceles Scalene  Types by Angle Equilateral Right Obtuse Acute Equilateral Right Isosceles.

Published byStephanie Blake Modified over 8 years ago

Similar presentations

Presentation on theme: "6/22/20161 2 Types of Triangles  Types by Length Equilateral Isosceles Scalene  Types by Angle Equilateral Right Obtuse Acute Equilateral Right Isosceles."— Presentation transcript:

1

2 6/22/20161

3 2 Types of Triangles  Types by Length Equilateral Isosceles Scalene  Types by Angle Equilateral Right Obtuse Acute Equilateral Right Isosceles Scalene Equilateral Obtuse Acute

4 6/22/20163 Right Triangles  Legs Shorter sides of triangle  Hypotenuse Longer side of triangle Side opposite right angle Hypotenuse leg

5 6/22/20164 Pythagoras Born: about 569 BC in Samos, Iona, Greece Died: about 475 BC  Greek philosopher  Mathematician  Most Known For: Sum of Angles of a Triangle Pythagorean Theorem Constructing Figures of a Given Area and Geometric Algebra Discovery of Irrational #s The 5 Regular Solids Whole Number Ratios of Consonant Intervals Musica Mundana

6 6/22/20165 Pythagorean Theorem  If the triangle had a right angle (90°)... ... and you made a square on each of the three sides, then... ... the biggest square had the exact same area as the other two squares put together! Proof of the Pythagorean Theorem

7 6/22/20166 Pythagorean Example  The formal equation is: a 2 + b 2 = c 2 “a” and “b” are the two legs “c” is the hypotenuse  TRY THIS: a = 3 b = 4 c = 5 a 2 + b 2 = c 2 3 2 + 4 2 = 5 2 Calculating this becomes: 9 + 16 = 25 yes, it works !

8 6/22/20167 More Examples  Find c in : a 2 + b 2 = c 2 where a = 5 and b = 12 5 2 + 12 2 = c 2 25 + 144 = 169 c 2 = 169 c = √169 c = 13  Find b in : a 2 + b 2 = c 2 where a = 9 and c = 15 9 2 + b 2 = 15 2 81 + b 2 = 225 Take 81 from both sides b 2 = 144 b = √144 b = 12

9 6/22/20168 Pythagorean Triples  A "Pythagorean Triple“ a set of three numbers a,b,c such that a²+b²=c². Pythagoras proved that the sides of a right triangle have this relationship He then went crazy after discovering that the sides of a right triangle aren't always rational.

10 6/22/20169 Real - Life Application TV screens & computer monitors are measured on the diagonal

11 6/22/201610 Resources  http://www.mathsisfun.com/pythagoras.html http://www.mathsisfun.com/pythagoras.html  http://www.nadn.navy.mil/MathDept/mdm/pyth.html http://www.nadn.navy.mil/MathDept/mdm/pyth.html  http://www.screenmath.com/ http://www.screenmath.com/  http://mcraeclan.com/mathhelp/Pythag.htm http://mcraeclan.com/mathhelp/Pythag.htm  http://scienceworld.wolfram.com/biography/Pythagoras.html http://scienceworld.wolfram.com/biography/Pythagoras.html

Download ppt "6/22/20161 2 Types of Triangles  Types by Length Equilateral Isosceles Scalene  Types by Angle Equilateral Right Obtuse Acute Equilateral Right Isosceles."

Similar presentations

Pythagoras Pythagoras was a Greek scholar and philosopher in the late century BC. Known as “the father of numbers, his teachings covered a variety of areas.

Pythagoras Pythagoras was a Greek scholar and philosopher in the late century BC. Known as “the father of numbers, his teachings covered a variety of areas.
Pythagoras Pythagoras was a Greek scholar and philosopher ca 548 BC to 495 BC. Known as “the father of numbers, his teachings covered a variety of areas.

Pythagoras Pythagoras was a Greek scholar and philosopher ca 548 BC to 495 BC. Known as “the father of numbers, his teachings covered a variety of areas.
The Pythagorean Theorem

The Pythagorean Theorem
The Pythagorean Theorem. The Right Triangle A right triangle is a triangle that contains one right angle. A right angle is 90 o Right Angle.

The Pythagorean Theorem. The Right Triangle A right triangle is a triangle that contains one right angle. A right angle is 90 o Right Angle.
10-4 The Pythagorean Theorem

10-4 The Pythagorean Theorem
Pythagorean Theorem. Pythagoras Born on the Greek Isle of Samos in the 6 th Century Lived from 569-500 BC He studied and made contributions in the fields.

Pythagorean Theorem. Pythagoras Born on the Greek Isle of Samos in the 6 th Century Lived from BC He studied and made contributions in the fields.
Pythagorean Theorem 2 Algebraic Proofs. Pythagoras’ Proof.

Pythagorean Theorem 2 Algebraic Proofs. Pythagoras’ Proof.
Geometry Section 9.4 Special Right Triangle Formulas

Geometry Section 9.4 Special Right Triangle Formulas
8-1 The Pythagorean Theorem and Its Converse. Parts of a Right Triangle In a right triangle, the side opposite the right angle is called the hypotenuse.

8-1 The Pythagorean Theorem and Its Converse. Parts of a Right Triangle In a right triangle, the side opposite the right angle is called the hypotenuse.
8.1 Pythagorean Theorem and Its Converse

8.1 Pythagorean Theorem and Its Converse
7.1 – Apply the Pythagorean Theorem. Pythagorean Theorem: leg hypotenuse a b c c 2 = a 2 + b 2 (hypotenuse) 2 = (leg) 2 + (leg) 2 If a triangle is a right.

7.1 – Apply the Pythagorean Theorem. Pythagorean Theorem: leg hypotenuse a b c c 2 = a 2 + b 2 (hypotenuse) 2 = (leg) 2 + (leg) 2 If a triangle is a right.
THE PYTHAGOREAN THEOREM A 2 + B 2 = C 2. THE PYTHAGOREAN THEOREM LEG A LEG B HYPOTENUSE PARTS OF A RIGHT TRIANGLE.

THE PYTHAGOREAN THEOREM A 2 + B 2 = C 2. THE PYTHAGOREAN THEOREM LEG A LEG B HYPOTENUSE PARTS OF A RIGHT TRIANGLE.
The Pythagorean Theorem

The Pythagorean Theorem
The World Of Triangles Juliána Melicherová University of Pavol Jozef Šafárik, Košice.

The World Of Triangles Juliána Melicherová University of Pavol Jozef Šafárik, Košice.
The World Of Triangles. Triangles A triangle is a 3- sided polygon. Every triangle has three sides and three angles. When added together, the three angles.

The World Of Triangles. Triangles A triangle is a 3- sided polygon. Every triangle has three sides and three angles. When added together, the three angles.
Section 8-1: The Pythagorean Theorem and its Converse.

Section 8-1: The Pythagorean Theorem and its Converse.
4.7 – Square Roots and The Pythagorean Theorem. SQUARES and SQUARE ROOTS: Consider the area of a 3'x3' square: A = 3 x 3 A = (3) 2 = 9.

4.7 – Square Roots and The Pythagorean Theorem. SQUARES and SQUARE ROOTS: Consider the area of a 3'x3' square: A = 3 x 3 A = (3) 2 = 9.
- Four sides - Four angles - Four vertices  - The diagonals are equal in length and perpendicular and bisect each other.

- Four sides - Four angles - Four vertices  - The diagonals are equal in length and perpendicular and bisect each other.
Modeling Pythagorean Theorem - Geometrically. Template.

Modeling Pythagorean Theorem - Geometrically. Template.
Objective The student will be able to:

Objective The student will be able to:

Similar presentations

Ads by Google