Pythagorean Theorem Obj: SWBAT identify and apply the Pythagorean Thm and its converse to find missing sides and prove triangles are right Standard: M11.C.1.4.1.

Slides:

Advertisements

Similar presentations

Apply the Pythagorean Theorem Chapter 7.1. Sides of a Right Triangle Hypotenuse – the side of a right triangle opposite the right angle and the longest.

Advertisements

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 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.

Lesson 10.1 The Pythagorean Theorem. The side opposite the right angle is called the hypotenuse. The other two sides are called legs. We use ‘a’ and ‘b’

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

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.

Pythagorean Theorem and Its Converse Objective To use the Pythagorean Theorem and its converse Essential Understanding: If you know the lengths of any.

8.1 Pythagorean Theorem and Its Converse

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

8.1 The Pythagorean Theorem and Its Converse. Pythagorean Theorem In a right triangle, the sum of the squares of the lengths of the legs is equal to the.

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.

+ Warm Up B. + Homework page 4 in packet + #10 1. Given 2. Theorem Given 4. Corresponding angles are congruent 5. Reflexive 6. AA Similarity 7.

Pythagorean Theorum Shaikh albuainain. The Pythagorean theorem has its name derived from the ancient Greek mathematician Pythagoras (569 BC-500 BC). Pythagoras.

8-1 The Pythagorean Theorem and Its Converse.

Unit 8 Lesson 9.2 The Pythagorean Theorem CCSS G-SRT 4: Prove theorems about triangles. Lesson Goals Use the Pythagorean Th. to find missing side lengths.

Section 8-1: The Pythagorean Theorem and its Converse.

Bellwork 1) 2) 3) Simplify. Lesson 7.1 Apply the Pythagorean Theorem.

Section 10.3 The Pythagorean Theorem

Goal 1: To use the Pythagorean Theorem Goal 2: To use the Converse of the Pythagorean Theorem.

Learning Pythagoras theorem

The Pythagorean Theorem and Its Converse OBJECTIVE: To use the Pythagorean Theorem and its converse BIG IDEAS: MEASUREMENT REASONING AND PROOF ESSENTIAL.

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.

Right Triangles A triangle is the simplest polygon in a plane, consisting of three line segments There are many uses of the triangle, especially in construction.

OBJECTIVE I will use the Pythagorean Theorem to find missing sides lengths of a RIGHT triangle.

Pythagorean Theorem - Thurs, Oct 7

Pythagorean Theorem What is it and how does it work? a 2 + b 2 = c 2.

Objectives: 1) To use the Pythagorean Theorem. 2) To use the converse of the Pythagorean Theorem.

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

3/11-3/ The Pythagorean Theorem. Learning Target I can use the Pythagorean Theorem to find missing sides of right triangles.

Click on Geometry Click on Plane Geometry Scroll down to Pythagoras’ Theorem and Pythagorean Triples You will need both of these.

Pythagorean Theorem OBJ: to use the Pythagorean theorem to solve problems.

Introduction to Chapter 4: Pythagorean Theorem and Its Converse

Warm Up Simplify the square roots

8.1 Pythagorean Theorem and Its Converse

The Pythagorean Theorem

Pythagorean Triples.

Pythagorean Theorem and it’s Converse

Pythagorean Theorem and Its Converse

Rules of Pythagoras All Triangles:

The Pythagorean Theorem

Pythagoras’ Theorem – Outcomes

Section 7.2 Pythagorean Theorem and its Converse Objective: Students will be able to use the Pythagorean Theorem and its Converse. Warm up Theorem 7-4.

Bellringer Simplify each expression 5 ∙ ∙ 8.

7.2 The Pythagorean Theorem and its Converse

Pythagorean Theorem and Its Converse

Math 3-4: The Pythagorean Theorem

9-2 Pythagorean Theorem.

8-2 The Pythagorean Theorem and Its Converse

8.1 Pythagorean Theorem and Its Converse

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

The Pythagorean Theorem

9.2 The Pythagorean Theorem

Pythagorean Theorem a²+ b²=c².

8.1 Pythagorean Theorem and Its Converse

11.7 and 11.8 Pythagorean Thm..

The Pythagorean Theorem and Its Converse

PYTHAGOREAN THEOREM VOCABULARY.

The Pythagorean Theorem and Its Converse

Warm Up Classify each triangle by its angle measures. 3. Simplify

Pythagorean Theorem What is it and how does it work? a2 + b2 = c2.

Pythagoras’ Theorem.

Geometric Mean and the Pythagorean Theorem

The Pythagorean Theorem

REVIEW LEG HYPOTENUSE LEG.

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.

Pythagorean Theorem By: Mikayla Moore.

7-2 PYTHAGOREAN THEOREM AND ITS CONVERSE

Presentation transcript:

Pythagorean Theorem Obj: SWBAT identify and apply the Pythagorean Thm and its converse to find missing sides and prove triangles are right Standard: M11.C.1.4.1 Find the measure of a side of a right triangle using the Pythagorean Thm

History of the Pythagorean Thm At the height of their power, nearly a millennium before Pythagoras, circa 1900 - 1600 BCE , the Babylonians (Babylon located in modern day Iraq) identify what are now called Pythagorean triples (a set of positive integers a, b, c such that a2 + b2 = c2

History of the Pythagorean Thm A Chinese astronomical and mathematical treatise called the Chou Pei Suan Ching (The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven, ca. 500-200 B.C.), possibly predating Pythagoras, gives a statement of and geometrical demonstration of the Pythagorean Thm.

History of the Pythagorean Thm Despite evidence predating him, the Greek named Pythagoras is credited with the theorem. According to tradition, Pythagoras once said, “Number rules the universe…” WHAT A FREAKING GENIUS!!!!

Basics of the Right Triangle hypotenuse leg leg Right angle

Pythagorean Thm In ANY right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. a2 + b2 = c2

Use the Pythagorean Thm to solve for x. 3 4

1. Square both legs 1 2 3 4 5 6 7 8 4 ft 9 10 11 12 13 14 15 16 3 ft 4ft 1 2 3 4 5 6 3 ft 7 8 9

2. Count the total squares 1 2 3 4 5 6 7 8 4 ft 9 10 11 12 13 14 15 16 3 ft 4ft 1 2 3 9 + 16 = 25 4 5 6 3 ft 7 8 9

3. Put that number of squares on the hypotenuse 2 4 6 8 10 12 14 16 18 20 22 24 1 3 5 7 9 11 13 15 17 19 21 23 25 3 ft 4 ft 4ft 1 3 4 5 6 7 8 9 2 10 11 12 13 14 15 16 9 + 16 = 25

4. Count the number of squares that touch the hypotenuse. 2 4 6 8 10 12 14 16 18 20 22 24 1 3 5 7 9 11 13 15 17 19 21 23 25 3 ft 4 ft 4ft 1 3 4 5 6 7 8 9 2 10 11 12 13 14 15 16 9 + 16 = 25 # = 5

5.That number is the length of the hypotenuse. 2 4 6 8 10 12 14 16 18 20 22 24 1 3 5 7 9 11 13 15 17 19 21 23 25 3 ft 4 ft 4ft 1 3 4 5 6 7 8 9 2 10 11 12 13 14 15 16 9 + 16 = 25 # = 5 Length = 5

WOW, it’s actually the Pythagorean Thm! That’s so freaking cool!!! LOOK FAMILIAR?!

Why are the wrong answers wrong???

Pythagorean Triples Are short cuts! They are sets of 3 whole numbers (a, b, and c) that satisfy the equation a2 + b2 = c2 Most frequent examples: *** 3, 4, 5 (where a=3, b=4, c=5) *** 5, 12, 13 8, 15, 17 7, 24, 25 ANY scale or multiple of Pythagorean triples will work!!!

Pythagorean Triple Example

Don’t be fooled by the disguise… ...it’s still the Pythagorean Thm!!

Pythagorean Thm application with even more Geometry Pythagorean Thm application with even more Geometry!!! It’s actually that much more fun!!!

HOLY SMOKES, LOOK AT ALL OF THIS GEOMETRY!!! A-MAZ-ING!!!!