Pythagorean Triples. 43210 In addition to level 3.0 and beyond what was taught in class, the student may:  Make connection with other concepts in math.

Slides:

Advertisements

Similar presentations

Proving the Distance Formula

Advertisements

Pythagorean Relationship 2 (Finding the length of the Hypotenuse)

The Pythagorean Theorem Presented by: Tanya Van Dam Kalles Junior High Algebra 2 Spring 2000.

Locating Points & Finding Distances

Introduction It is not uncommon for people to think of geometric figures, such as triangles and quadrilaterals, to be separate from algebra; however, we.

Pythagorean Theorem Please view this tutorial and answer the follow-up questions on loose leaf to turn in to your teacher.

Finding Distance by using the Pythagorean Theorem

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.

Using the Pythagorean Theorem in 3-Dimensional Shapes.

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. The Right Triangle A right triangle is a triangle that contains one right angle. A right angle is 90 o Right Angle.

Bell Work: Use the difference of two squares theorem to write the answers to the following equation. w = 14 2.

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

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

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

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 called legs. The side.

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

Pythagorean Theorem 5.4. Learn the Pythagorean Theorem. Define Pythagorean triple. Learn the Pythagorean Inequality. Solve problems with the Pythagorean.

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 Theorem 8th Math Presented by Mr. Laws

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.

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.

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.

Geometric Mean and the Pythagorean Theorem

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.

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

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

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.

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.

Bell Ringer What is the measurement of the missing angles? 38˚ b a c d a = 142°, supplementary b = 142°, alternate interior angle c = 38°, corresponding.

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.

Pythagorean Theorem & its Converse 8 th Grade Math Standards M.8.G.6- Explain a proof of the Pythagorean Theorem and its converse. M.8.G.7 - Apply the.

The Pythagorean Theorem

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.

Using the Pythagorean Theorem in 3-Dimensional Shapes

8.1 Pythagorean Theorem and Its Converse

Pythagorean Triples.

Pythagorean Theorem and it’s Converse

Pythagorean theorem.

Midpoint and Distance in the Coordinate Plane

Right Triangle The sides that form the right angle are called the legs. The side opposite the right angle is called the hypotenuse.

Practice, Practice, Practice!

The Pythagorean Theorem

Sect. 9.2 & 9.3 The Pythagorean Theorem

7.2 The Pythagorean Theorem and its Converse

Introduction It is not uncommon for people to think of geometric figures, such as triangles and quadrilaterals, to be separate from algebra; however, we.

Pythagorean Theorem and Distance

Math 3-4: The Pythagorean Theorem

Objectives Use the Pythagorean Theorem and its converse to solve problems. Use Pythagorean inequalities to classify triangles.

9-2 Pythagorean Theorem.

PYTHAGOREAN THEOREM VOCABULARY.

P.5 The Cartesian Plane Our goals are to learn

6-3 The Pythagorean Theorem Pythagorean Theorem.

8-2 The Pythagorean Theorem and Its Converse

PROVING THE PYTHAGOREAN THEOREM

Chapter 1: Lesson 1.1 Rectangular Coordinates

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

5-3: The Pythagorean Theorem

PYTHAGOREAN THEOREM VOCABULARY.

Geometric Mean and the Pythagorean Theorem

The Pythagorean Theorem

Using Coordinates to Prove Geometric Theorems with Slope and Distance

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

Presentation transcript:

Pythagorean Triples

43210 In addition to level 3.0 and beyond what was taught in class, the student may:  Make connection with other concepts in math.  Make connection with other content areas.  Explain the relationship between the Pythagorean Theorem and the distance formula. The student will understand and apply the Pythagorean Theorem.  Prove the Pythagorean Theorem and its converse.  Apply the Pythagorean Theorem to real world and mathematical situations.  Find the distance between 2 points on a coordinate plane using the Pythagorean Theorem. The student will understand the relationship between the areas of the squares of the legs and area of the square of the hypotenuse of a right triangle.  Explain the Pythagorean Theorem and its converse.  Create a right triangle on a coordinate plane, given 2 points. With help from the teacher, the student has partial success with level 2 and level 3 elements.  Plot 3 ordered pairs to make a right triangle  Identify the legs and the hypotenuse of a right triangle Find the distance between 2 points on the coordinate grid (horizontal and vertical axis). Even with help, students have no success with the unit content. Focus 5 - Learning Goal #1: Students will understand and apply the Pythagorean Theorem.

Fact In a right triangle, the sides touching the right angle are called legs. The side opposite the right angle is the hypotenuse.

The Pythagorean Theorem, a 2 + b 2 = c 2, relates the sides of RIGHT triangles. a and b are the lengths of the legs and c is the length of the hypotenuse.

A Pythagorean Triple…  Is a set of three whole numbers that satisfy the Pythagorean Theorem. What numbers can you think of that would be a Pythagorean Triple? Remember, it has to satisfy the equation a 2 + b 2 = c 2.

Pythagorean Triple:  The set {3, 4, 5} is a Pythagorean Triple.  a 2 + b 2 = c 2  = 5 2  = 25  25 = 25

Show that {5, 12, 13} is a Pythagorean triple.  Always use the largest value as c in the Pythagorean Theorem.  a 2 + b 2 = c 2  = 13 2  = 169  169 = 169

Show that {2, 2, 5} is not a Pythagorean triple.  a 2 + b 2 = c 2  = 5 2  = 25  8 ≠ 25  Showing that three numbers are a Pythagorean triple proves that the triangle with these side lengths will be a right triangle.

How to find more Pythagorean Triples  If we multiply each element of the Pythagorean triple, such as {3, 4, 5} by another integer, like 2, the result is another Pythagorean triple {6, 8, 10}.  a 2 + b 2 = c 2  = 10 2  = 100  100 = 100

By knowing Pythagorean triples, you can quickly solve for a missing side of certain right triangles.  Find the length of side b in the right triangle below.  Use the Pythagorean triple {5, 12, 13}.  The length of side b is 5 units.

Find the length of side a in the right triangle below.  It is not obvious which Pythagorean triple these sides represent.  Begin by dividing the given sides by their GCF (greatest common factor)  { ___, 16, 20} ÷ 4  { ___, 4, 5}  We see this is a {3, 4, 5} Pythagorean triple.  Since we divided by 4, we must now do the opposite and multiple by 4.  {3, 4, 5} 4 = {12, 16, 20}  Side a is 12 units long.