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.

Slides:

Advertisements

Similar presentations

Measurement Pythagorean Relationship 3 (Finding the length of an unknown leg)

Advertisements

Pythagorean Relationship 2 (Finding the length of the Hypotenuse)

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

The Pythagorean Theorem leg hypotenuse leg Applies to Right Triangles only! The side opposite the right angle The sides creating the right angle are called.

Finding Distance by using the Pythagorean Theorem

Created by G. Antidormi 2003 The Pythagorean Theorem.

EXAMPLE 4 SOLUTION Method 1: Use a Pythagorean triple. A common Pythagorean triple is 5, 12, 13. Notice that if you multiply the lengths of the legs of.

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 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.

Lesson 56: Special Right Triangles

EXAMPLE 1 Find the length of a hypotenuse SOLUTION Find the length of the hypotenuse of the right triangle. (hypotenuse) 2 = (leg) 2 + (leg) 2 Pythagorean.

EXAMPLE 1 Find the length of a hypotenuse SOLUTION Find the length of the hypotenuse of the right triangle. (hypotenuse) 2 = (leg) 2 + (leg) 2 Pythagorean.

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’

10.5 – The Pythagorean Theorem. leg legleg hypotenuse hypotenuse leg legleg.

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

MA.912.G.5.1 : Apply the Pythagorean Theorem and its Converse. A.5 ft B.10 ft C. 15 ft D. 18 ft What is the value of x? x 25 ft 20 ft.

Pythagorean Theorem Use the Pythagorean Theorem to find the missing length of the right triangle. 1.

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.

Right Triangles And the Pythagorean Theorem. Legs of a Right Triangle Leg -the two sides of a right triangle that form the right angle Leg.

Section 3-5 p. 137 Goal – to solve problems using the Pythagorean Theorem.

7.1 – Apply the Pythagorean Theorem. Pythagorean Theorem: leg hypotenuse a b c c 2 = a 2 + b 2 (hypotenuse) 2 = (leg) 2 + (leg) 2 If a triangle is a right.

12.3 The Pythagorean Theorem

Pythagorean Theorem 8th Math Presented by Mr. Laws

Objective The student will be able to:

6-3 The Pythagorean Theorem Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.

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

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.

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

11.4 Pythagorean Theorem Definitions Pythagorean Theorem

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.

4.4 Pythagorean Theorem and the Distance Formula Textbook pg 192.

Converse of Pythagorean Theorem

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

Pythagorean Theorem Converse Special Triangles. Pythagorean Theorem What do you remember? Right Triangles Hypotenuse – longest side Legs – two shorter.

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.

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.

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

 Right Triangle – A triangle with one right angle.  Hypotenuse – Side opposite the right angle and longest side of a right triangle.  Leg – Either.

The Pythagorean Theorem

Midpoint And Distance in the Coordinate Plane

LT 5.7: Apply Pythagorean Theorem and its Converse

Standard: MG 3.3 Objective: Find the missing side of a right triangle.

12-2 The Pythagorean Theorem

4.5 The Converse of the Pythagorean Theorem

Math 3-4: The Pythagorean Theorem

Notes Over Pythagorean Theorem

11.4 Pythagorean Theorem.

Section 5.5: Special Right Triangles

4.3 The Rectangle, Square and Rhombus The Rectangle

6.2: Pythagorean Theorem Objectives:

6-3 The Pythagorean Theorem Pythagorean Theorem.

5-7 The Pythagorean Theorem

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

7.0: Pythagorean Theorem Objectives:

4.3 The Rectangle, Square and Rhombus The Rectangle

The Pythagorean Theorem

10.3 and 10.4 Pythagorean Theorem

Pythagorean Theorem a²+ b²=c².

G3.2 Pythagorean Theorem Objectives:

4-6 Congruence in Right Triangles

6.5 Pythagorean Theorem.

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

Chapter 3: Solving Equations

Similar Triangles Review

The Pythagorean Theorem

10-1 The Pythagorean Theorem

Triangle Relationships

Complete the Thursday WAM. *Writing about Math*

Presentation transcript:

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 Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Back to the Basics Right Triangles need to have one 90° angle Right Triangles have 2 legs and a hypotenuse.

Converse of the Pythagorean Theorem 5² + 12² = 13² = = 169 4² + 5² = 6² = ǂ 36