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.

Slides:

Advertisements

Similar presentations

© Project Maths Development Team

Advertisements

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

Quit Introduction Pythagoras Proof of Theorem Quit 5 2 = In a right-angled triangle, the square on the hypotenuse is equal to the sum of the.

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.

Pythagorean Theorem By: Tytionna Williams.

Slide The Pythagorean Theorem and the Distance Formula  Special Right Triangles  Converse of the Pythagorean Theorem  The Distance Formula: An.

The Pythagorean Theorem Converse & Triangle Inequality Theorem  Pythagoras, circa 570 BC.

9.2 The Pythagorean Theorem

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

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.

Geometry 4.4 SWLT: Use the Pythagorean Theorem to find side lengths of Right Triangles.

12.3 The Pythagorean Theorem

PYTHAGOREAN THEOREAM

A Cheerful Fact: The Pythagorean Theorem Presented By: Rachel Thysell.

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.

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.

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle.

Pythagorean Theorem Proof Unit 4 Project Grace Olson.

z Hypotenuse x y x 2 = y 2 + z 2 Right Angle Triangle x y x 2 > y 2 + z 2 Obtuse Triangle z xy x 2 < y 2 + z 2 z Acute Triangle Pythagoras.

Pythagorean Theorem Unit 7 Part 1. The Pythagorean Theorem The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

The Pythagorean Theorem

The Theorem Of Pythagoras Pythagoras was a Greek Mathematician.( B.C) years old is even older than your teacher. He was eccentric. (mad!!)

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

Similar Triangles and Pythagorean Theorem Section 6.4.

The Pythagorean Theorem Use the Pythagorean Theorem to find the missing measure in a right triangle including those from contextual situations.

Section 8-3 The Converse of the Pythagorean Theorem.

Pythagorean Theorem Proof 8th Math Presented by Mr. Laws

Exploring. Pythagorean Theorem For any right triangle, the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the.

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.

Pythagoras by: Alyssa Parrish. Pythagoras Greek philosopher and mathematician born on the island of Samos,Ionia.

Pythagoras Theorem Proof of the Pythagorean Theorem using Algebra.

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

Find: (to 1.d.p) a)3² = b) 7² = c) 3.45² = d) 9² = e) 10² = f) 20² = g) 2.1 ² = Find: a)√9 = b) √7 = c) √36= d) √2= e) √1.456 = f) √2.5 g) √64 =

10-1 The Pythagorean Theorem. LEGS Hypotenuse Problem 1: Finding the Length of a Hypotenuse The tiles shown below are squares with 6-in. sides. What.

The Pythagorean Theorem

Who wants to be a Millionaire? Pythagorean Triads.

@ Dr.K.Thiyagu, CUTN Pythagoras Dr.K.Thiyagu, CUTN5.

Converse of the Pythagorean Theorem

Rules of Pythagoras All Triangles:

The Pythagorean Theorem

Pythagoras’ Theorem – Outcomes

January 13th 2010 Bring it on Pythagoras.

Cell phone use is prohibited.

Pythagorean Theorem.

Theorem The area A of a triangle is

5.4: The Pythagorean Theorem

Pythagoras’ Theorem… ...a pictorial proof Carmelo Ellul

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

Pythagorean Theorem a²+ b²=c².

5.4: The Pythagorean Theorem

Pythagoras Theorem © T Madas.

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

Similar Triangles Review

Pythagoras’ Theorem.

The Pythagorean Theorem

The Pythagorean Theorem

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.

10-1 The Pythagorean Theorem

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

Converse to the Pythagorean Theorem

Presentation transcript:

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 of the squared of both sides.

Pythagorean theorem proof of the oldest

Proof 1 1. Δ BAF All equal DAC(SAS) 2. Area of ACGF ＝ 2× Area of Δ BAF ＝ 2× Area of Δ DAC 3. Area of AMLD ＝ 2× Area of Δ DAC 4. ∴ Area of ACGF ＝ Area of AMLD 5. Same Reason Area of BCHK ＝ Area of BMLE 6. ∴ Area of ACGF ＋ Area of BCHK ＝ Area of ABED Scilicet ： AC 2 ＋ BC 2 ＝ AB 2

Proof 2 Below left are two large squares of equal area Also lost four identical right-angled triangle Scilicet ：弦 2 ＝勾 2 ＋股 2

Problem How to use the three squares to prove the Pythagorean Theorem?