Warm up 1. 3. 2..

Slides:

Advertisements

Similar presentations

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

Advertisements

Things to do: ♥Make a new note book ♥Get out your homework (triangle worksheet)

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.

Pythagorean Theorem Formula: a2 + b2 = c2 This formula helps determine two things: the lengths of the different sides of a right triangle, and whether.

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 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.

10-4 The Pythagorean Theorem

The Pythagorean Theorem. 8/18/20152 The Pythagorean Theorem “For any right triangle, the sum of the areas of the two small squares is equal to the area.

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.

11.2 Pythagorean Theorem. Applies to Right Triangles Only! leg Leg a hypotenuse c Leg b.

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’

4.4: THE PYTHAGOREAN THEOREM AND DISTANCE FORMULA

9.2 The Pythagorean Theorem

Pythagorean Theorem Mr. Parks Algebra Support. Objective The student will be able to: Find the missing side of a right Triangle using the Pythagorean.

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.

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

Objective The student will be able to:

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

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

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.

Things to remember: Formula: a 2 +b 2 =c 2 Pythagorean Theorem is used to find lengths of the sides of a right triangle Side across from the right angle.

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.

This is a right triangle: We call it a right triangle because it contains a right angle.

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.

Pythagorean Theorem and it’s Converse. Pythagorean Theorem Pythagorean Theorem: used for right triangles, it is a tool used to solve for a missing side.

4.4 Pythagorean Theorem and the Distance Formula Textbook pg 192.

THE PYTHAGOREAN THEOREM AND AREA OF A TRIANGLE. Warm – Up!! Good Morning! As you walk in, get your calculator and pick up your guided notes from the podium.

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

Pythagorean Theorem SOL 8.10 cont.. Review Previously, we used the Pythagorean Theorem to find the hypotenuse of a right triangle. (a 2 + b 2 = c 2 )

Warm up Make a chart in your notes of the perfect squares from 1 to 20. For Example: 1 2 = = 4.

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.

 Remember the pattern for right triangles: Area of small square + Area of medium square = Area of large square.

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.

Pythagorean Theorem and Special Right Triangles. Anatomy of a Right Triangle Why is a right triangle called a right triangle? Because it is a triangle.

Pythagorean Theorem. What is a right triangle? It is a triangle which has an angle that is 90 degrees. The two sides that make up the right angle are.

Essential Question: What is the Pythagorean Theorem and what is it used for? PythagoreanPa-THAG- oh- REE-an.

Objective: To use the Pythagorean Theorem to solve real world problems. Class Notes Sec 9.2 & a b c a short leg b long leg c hypotenuse 2. Pythagorean.

Pythagorean Theorem.

Pythagorean Triples.

Pythagorean Theorem and it’s Converse

Pythagorean theorem.

The Right Triangle and The Pythagorean Theorem

Objective The student will be able to:

The Pythagorean Theorem

9-2 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?

6-3 The Pythagorean Theorem Pythagorean Theorem.

The Pythagorean Theorem

The Pythagorean Theorem

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

5-3: The Pythagorean Theorem

9.2 The Pythagorean Theorem

Page 134 First, some definitions.

Pythagorean Theorem a²+ b²=c².

Use the Pythagorean Theorem to find a Leg

Objective Students will be able to:

Solve for the unknown side or angle x

Geometric Mean and the Pythagorean Theorem

Objective The student will be able to:

Objective The student will be able to:

The 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.

Chapter 10 Vocabulary 1.) hypotenuse 2.) leg 3.) Pythagorean Theorem

Presentation transcript:

Warm up 1. 3. 2.

Pythagorean Theorem Pythagoras was a Greek philosopher and teacher He lived from 569 to 495 B. C. Often described as the “first pure mathematician”

Pythagorean theorem – only “works” for right triangles For right triangles, where a and b are the legs and c is the hypotenuse of the triangle. There are more than 200 known proofs. Check out a proof of the Theorem online at http://www.keymath.com/x19481.xml Hypotenuse (c) across from the “box” Leg (b) Leg (a)

Ex1: 10 6 x a b Identify your hypotenuse ( c ) The other two sides are legs (it doesn’t matter which on you assign a or b Plug into formula Remember order of operations - SQUARE sides first and solve c 62 + x2 = 102 36 + x2 = 100 -36 x2 = 64 x = 8

Example How high up a wall will a 20’ ladder touch if the ladder is placed 5’ from the wall? Step 1: Identify the hypotenuse and label it “c” Wall Ladder 20’ Step 2: Label the other two sides as “a” and “b” hypotenuse b c Step 3: Plug in and solve. 5’ a or

Ex3: y c a b Follow the steps -5

Classwork Solve for the missing side. Ex. 1 Ex. 2 5 x y = 3 1 Ex. 3 4 2 6 z = 5

Pythagorean Triples Any three positive integers which fit the Pythagorean equation are called Pythagorean Triples. Common Pythagorean Triples are… 3, 4, 5 5, 12, 13 7, 24, 25

Homework Worksheet