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.

Slides:

Advertisements

Similar presentations

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

Advertisements

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.

Created by G. Antidormi 2003 The Pythagorean Theorem.

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.

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.

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’

Pythagorean Theorem By: Tytionna Williams.

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.

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.

Algebra 12.5 The Pythagorean Theorem. Radical Review  Simplify each expression. You try! = 5 = 8/3 = 28 = 9/5.

+ 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.

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.

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.

Pythagorean Theorem. Pythagoras of Samos Birth: 570 B.C.E Samos, Greece Death: 495 B.C.E.

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.

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.

Chapter 1: Square Roots and the Pythagorean Theorem Unit Review.

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.

The Distance and Midpoint Formulas Unit 8. Warm – Up!! As you walk in, please pick up your calculator and begin working on your warm – up!! 1. Use the.

RIGHT TRIANGLES A RIGHT TRIANGLE is a triangle with one right angle. a b c Sides a and b are called legs. Side c is called the hypotenuse.

Pythagorean Theorem and Its Converse Chapter 8 Section 1.

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.

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.

Objective The student will be able to: use the Pythagorean Theorem Designed by Skip Tyler, Varina High School.

8-6 and 8-7 Square Roots, Irrational Numbers, and 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.

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

Warm Up Simplify the square roots

The Pythagorean Theorem

Pythagorean Triples.

Pythagorean Theorem and it’s Converse

Pythagorean theorem.

The Distance and Midpoint Formulas

Objective The student will be able to:

The Pythagorean Theorem

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.

7.2 The Pythagorean Theorem and its Converse

7.1 Apply the Pythagorean Theorem

Math 3-4: The Pythagorean Theorem

Objective The student will be able to:

6-3 The Pythagorean Theorem Pythagorean Theorem.

8-2 The Pythagorean Theorem and Its Converse

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

5-3: The Pythagorean Theorem

7-1 and 7-2: Apply the Pythagorean Theorem

Solve for the unknown side or angle x

Geometric Mean and the Pythagorean Theorem

Objective The student will be able to:

The Pythagorean Theorem

Objective The student will be able to:

Objective The student will be able to:

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.

Objective The student will be able to:

10-1 The Pythagorean Theorem

7-2 PYTHAGOREAN THEOREM AND ITS CONVERSE

Presentation transcript:

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. Go ahead and label your triangle based on the definitions below (be sure to fill in the definitions too!):  Hypotenuse – the side of a right triangle opposite the right angle and the longest side.  Legs – the sides of a right triangle that are not the hypotenuse.

THE PYTHAGOREAN THEOREM In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the legs.

IF I AM GIVEN 2 SIDES OF A RIGHT TRIANGLE MAKE UP THE SIDES OF PYTHAGOREAN TRIPLE, HOW DO YOU FIND THE MISSING SIDE? There are 2 possible scenarios: 1. You are given both legs of the right triangle and need to solve for the hypotenuse. 2. You are given one leg and one hypotenuse and need to solve for the other leg.

EXAMPLE 1: USE THE PYTHAGOREAN THEOREM TO FIND THE HYPOTENUSE. 68x²x² = x ² 100= x ²

EXAMPLE 2: USE THE PYTHAGOREAN THEOREM TO FIND THE HYPOTENUSE.

PYTHAGOREAN TRIPLES  A Pythagorean Triple is a set of 3 positive integers or whole numbers that satisfies the Pythagorean theorem.

IS IT A PYTHAGOREAN TRIPLE? 33, 4, and 5 221, 28, and 35 330, 72, and 91 114, 48, and 50 yes no yes

EXAMPLE 3: FIND THE MISSING LEG x3 5² x ² + 9 = 25 x ² = 16

YOU TRY!! FIND THE MISSING LEG

FIND THE AREA WHEN GIVEN A LEG AND THE HYPOTENUSE 1. Find the other leg by plugging the known values into the Pythagorean Theorem. 2. Use the 2 legs in the formula for area of a triangle  A = ½BH

Find the perimeter of a triangle by adding the sides.  P = a + b + c, where a, b, and c are sides  Example:

FIND THE AREA OF THE TRIANGLE What is the formula for the area of a triangle? A = ½bh How will we find the height?

Find the Area of the Triangle

YOU TRY!! FIND THE AREA WHEN GIVEN A LEG AND A HYPOTENUSE. 8 16

YOU TRY!! FIND THE AREA WHEN GIVEN A LEG AND A HYPOTENUSE