Learning Pythagoras theorem

Slides:



Advertisements
Similar presentations
Pythagoras Bingo. Pick 8 from the list C no 16124yes Pythagorean triple Hypotenuse Pythagoras theorem.
Advertisements

The Pythagorean Theorem leg hypotenuse leg Applies to Right Triangles only! The side opposite the right angle The sides creating the right angle are called.
The Pythagorean theorem
 The Pythagorean theorem was named for its creator the Greek mathematician, Pythagoras. It is often argued that although named after him, the knowledge.
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.
The Pythagorean Theorem
EXAMPLE 4 Find the length of a hypotenuse using two methods SOLUTION Find the length of the hypotenuse of the right triangle. Method 1: Use a Pythagorean.
The Pythagorean Theorem
The Pythagorean Theorem Objective: Find the length of a using the Pythagorean Theorem.
Pythagorean Theorem 2 Algebraic Proofs. Pythagoras’ Proof.
Pythagorean Theorem By: Tytionna Williams.
4.4: THE PYTHAGOREAN THEOREM AND DISTANCE FORMULA
9.2 The Pythagorean Theorem
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.
Benchmark 40 I can find the missing side of a right triangle using the Pythagorean Theorem.
The Pythagorean Theorem
Section 11.6 Pythagorean Theorem. Pythagorean Theorem: In any right triangle, the square of the length of the hypotenuse equals the sum of the squares.
Pythagorean Theorum Shaikh albuainain. The Pythagorean theorem has its name derived from the ancient Greek mathematician Pythagoras (569 BC-500 BC). Pythagoras.
Pythagorean Theorum Adham Jad. What is a triangle? How many sides does a triangle have? What is the sum of angles in a triangle? Background & Concept.
PYTHAGOREAN THEOREAM
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.
Objective The student will be able to:
THE PYTHAGOREAN THEOROM Pythagorean Theorem  What is it and how does it work?  a 2 + b 2 = c 2  What is it and how does it work?  a 2 + b 2 = c 2.
Pythagorean Theorem. Pythagoras of Samos Birth: 570 B.C.E Samos, Greece Death: 495 B.C.E.
Pythagorean Theorem Ramzy Alseidi. Pythagoras is often referred to as the first pure mathematician. He was born on the island of Samos, Greece in 569.
Pythagorean Theorem Rochelle Williams TEC 539 Grand Canyon University July 7, 2010.
Section 10.3 The Pythagorean Theorem
Goal 1: To use the Pythagorean Theorem Goal 2: To use the Converse of the Pythagorean Theorem.
Pythagorean Theorem By: Kierra Reber period 6 extra credit.
CHAPTER 8: RIGHT TRIANGLES 8.2 THE PYTHAGOREAN THEOREM.
College Algebra Section R.3 Geometry Review Objectives of this Section Use the Pythagorean Theorem and Its Converse Know Geometry Formulas.
Chapter 1: Square Roots and the Pythagorean Theorem Unit Review.
Topic 10 – Lesson 9-1 and 9-2. Objectives Define and identify hypotenuse and leg in a right triangle Determine the length of one leg of a right triangle.
Warm Up. 9.4 Geometry’s Most Elegant Theorem Pythagorean Theorem.
Trigonometry – Right Angled Triangles By the end of this lesson you will be able to identify and calculate the following: 1. Who was Pythagoras 2. What.
OBJECTIVE I will use the Pythagorean Theorem to find missing sides lengths of a RIGHT triangle.
Pythagorean Theorem What is it and how does it work? a 2 + b 2 = c 2.
The Pythagorean Theorem Use the Pythagorean Theorem to find the missing measure in a right triangle including those from contextual situations.
Pythagoras c² a² b² c a b c² = a² + b² has the same area as the two smaller squares added together. The large square + PYTHAGORAS THEOREM is applied to.
The Pythagorean Theorem The Ladder Problem. Right Triangles Longest side is the hypotenuse, side c (opposite the 90 o angle) The other two sides are the.
The Pythagorean Theorem
 Right Triangle – A triangle with one right angle.  Hypotenuse – Side opposite the right angle and longest side of a right triangle.  Leg – Either.
Find the area and perimeter of the rectangle.. Simplify each radical expression:
8.1 Pythagorean Theorem and Its Converse
The Pythagorean Theorem
The Distance and Midpoint Formulas
The Right Triangle and The Pythagorean Theorem
The Pythagorean Theorem
Pythagorean Theorem and Distance
Math 3-4: The Pythagorean Theorem
Warm up: Think About it! If the red, blue and green squares were made of solid gold; would you rather have the red square or both the blue and green square?
PYTHAGOREAN THEOREM VOCABULARY.
8-2 The Pythagorean Theorem and Its Converse
5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA
9.2 The Pythagorean Theorem
Pythagorean Theorem a²+ b²=c².
PYTHAGOREAN THEOREM VOCABULARY.
The Pythagorean Theorem and Its Converse
Pythagorean Theorem What is it and how does it work? a2 + b2 = c2.
If a triangle is a RIGHT TRIANGLE, then a2 + b2 = c2.
Pythagoras’ Theorem.
The Pythagorean Theorem
Pythagorean Theorem.
The Pythagorean Theorem
In a right triangle, the side opposite the right angle is called the hypotenuse. This side is always the longest side of a right triangle. The other.
The Pythagoras Theorem c a a2 + b2 = c2 b.
Maths Unit 23 – Pythagoras & Trigonometry
Presentation transcript:

Learning Pythagoras theorem

1. Pythagoras theorem ‘The Pythagorean theorem is named after the Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof, although it is often argued that knowledge of the theorem predates him. There is evidence that Babylonian mathematicians understood the formula, although there is little surviving evidence that they fitted it into a mathematical framework.’ http://en.wikipedia.org/wiki/Pythagorean_theorem

2. Algebraic equations Pythagoras is the use of a simple algebraic expression.

a2+b2=c2 3. pythagorean equation The number of the side times itself a2+b2=c2 The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c) Each letter (variable) represents a side

4. Right angled triangle This equation can only be used on a right angled triangle In a right angled triangle: the square of the hypotenuse is equal to the sum of the squares of the other two sides.

5. Breaking down the equation a2 = one length of the triangle b2 = another length of the triangle c2 = identified as the hypotenuse

6. Sides of a right-angled triangle HYPOTENUSE: The opposite side of the right angle in a right angled triangle, which is also the longest side. ADJACENT: Either of two sides having a common side and a common vertex. OPPOSITE: When two lines intersect, four angles are formed. The angles that are directly opposite to each other, can be vertically opposite angles and that are non-adjacent are the opposite angles.

7. Putting the equation into practice a2+b2=c2 x 72 + 42 = c2 7 x 7 = 49 4 x 4 = 16 49 + 16 = c2 Once the numbers have been squared, add a and b 49+16 = 65 65 = c2 Find the square root of both sides of the equation Square root of 65 = 8.06 Therefore c = 8.06 4 5