Pythagoras Theorem Proof of the Pythagorean Theorem using Algebra.

Slides:

Advertisements

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.

Advertisements

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 Proofs TEKS 8.07 (C): The student is expected to use pictures or models to demonstrate the Pythagorean Theorem.

Chapter 10 Measurement Section 10.4 The Pythagorean Theorem.

Proof of Pythagoras’s Theorem GCSE Higher. ‘Prove’ means what exactly? A proof in mathematics is a process of logical steps Each step makes a statement.

The Pythagorean Theorem x z y. For this proof we must draw ANY right Triangle: Label the Legs “a” and “b” and the hypotenuse “c” a b c.

The Pythagorean Theorem Objective: Find the length of a using the Pythagorean Theorem.

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.

The Pythagorean Theorem in 3D

1 9.1 and 9.2 The Pythagorean Theorem. 2 A B C Given any right triangle, A 2 + B 2 = C 2.

Benchmark 40 I can find the missing side of a right triangle using the Pythagorean Theorem.

Pythagorean Theorem This project dives into the Pythagorean theorem and its uses. It was developed by Aldo Prado in the Winter of c a b a² + b² =

MAT 115 PROJECT I PYTHAGOREAM THEOREM

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.

PYTHAGORAS THEOREM Pythagoras Theorem. a b c “C “ is the longest side of the triangle “a” and “b” are the two other sides a 2 +b 2 =c 2.

PYTHAGOREAN THEOREAM

January 13 th 2010 Bring it on Pythagoras. 3 The Pythagorean Theorem A B C Given any right triangle, A 2 + B 2 = C 2.

Pythagoras' Theorem

 Turn in your 12.1/12.2 worksheet.  Take a 9.1/9.2 worksheet from the front.  Take your graphing calculator.  In your notebook, list the trigonometric.

Pythagorean Theorem Proof Unit 4 Project Grace Olson.

Pythagorean Theorem The best known mathematical proof is named for Pythagoras.

Pythagorean theorem Pythagoras discovered the most famous ：『 a 2 + b 2 = c 2 』 In the right triangle, the squared of the hypotenuse is equal to the sum.

The Pythagorean Theorem

Warm Up. 9.4 Geometry’s Most Elegant Theorem Pythagorean Theorem.

M May Pythagoras’ Theorem The square on the hypotenuse equals the sum of the squares on the other two sides.

7.1 – Apply the Pythagorean Theorem. In your group, do the following: 1. Find the area of one of the four right triangles baba abab b a c.

4.7 – Square Roots and The Pythagorean Theorem Day 2.

World 1-1 Pythagoras’ Theorem. When adding the areas of the two smaller squares, a2a2 Using math we say c 2 =a 2 +b 2 b2b2 c2c2 their sum will ALWAYS.

If you draw squares on the two shorter sides…

Section 8-3 The Converse of the Pythagorean Theorem.

Pythagorean Theorem Proof 8th Math Presented by Mr. Laws

Name:________________________ Date:______________ 1 Chapter 11 Lesson 5 StandardAlgebra 1 standard 2.0 Understand and use the operation of taking a root.

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.

 A square is a shape with four equal sides  Example:  All its angles are ninety degrees.

EXAMPLE 4 Use the concurrency of angle bisectors In the diagram, N is the incenter of ABC. Find ND. SOLUTION By the Concurrency of Angle Bisectors of a.

The Pythagorean Theorem

Lesson 8-3 The Converse of the Pythagorean Theorem (page 295) Essential Question How can you determine whether a triangle is acute, right, or obtuse?

6.5 Proving the Pythagorean Theorem.  Objectives  Prove the Pythagorean Theorem using similar triangles  Prove the Converse of the Pythagorean Theorem.

The proofs of the Early Greeks 2800 B.C. – 450 B.C.

Lesson 35: Special Right Triangles and the Pythagorean Theorem

18.01 Area & Perimeter of Rectangles

The Pythagorean Theorem

The Converse of the Pythagorean Theorem

January 13th 2010 Bring it on Pythagoras.

Below is the equation for the Pythagorean theorem

Pythagorean Theorem.

Take the worksheet from the Chrombook cart.

PYTHAGORAS THEOREM Carmelo Ellul AB2 = AC2 + CB2

Notes Over Pythagorean Theorem

Similarity, Congruence, & Proofs

The Pythagorean Theorem

Pythagorean Theorem a²+ b²=c².

Unit 5: Geometric and Algebraic Connections

By: Mark Nakanishi Source: Cut-the-knot.com

Difference of Two Squares

THE PYTHAGOREAN THEOREM

If a triangle is a RIGHT TRIANGLE, then a2 + b2 = c2.

Examples of Mathematical Proof

Pythagoras’ Theorem.

The Pythagorean Theorem

Lesson 8.7: Proof of 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 PYTHAGOREAN THEOREM

The Pythagorean Theorem

The Pythagoras Theorem c a a2 + b2 = c2 b.

Presentation transcript:

Pythagoras Theorem Proof of the Pythagorean Theorem using Algebra

We can prove that a 2 + b 2 = c 2 There are four ‘abc’ triangles in this figure The big square formed by these triangles has a side a+b

Total area of the big square is A=(a+b)(a+b) The area of the smaller square (inside the big one) is A= c 2

The area of a triangle is A =½ab

The area of four triangles together is A = 4(½ab) = 2ab

So the area of the four triangles and the small square is A = c²+2ab

The area of the big square is equal to the area of the small square and four triangles So we have (a+b)(a+b)= c²+2ab a 2 +2ab+ b 2 = c²+2ab Subtract ‘2ab’ in both sides and we have a 2 + b 2 = c 2

Pythagoras Theorem 2 nd Proof

β c - bb c c S OR Q P yx a α P P RS R Q P S Q α α β β x y a a c + b 2c x y