Objective The learner will solve problems using the Pythagorean Theorem.

Slides:

Advertisements

Similar presentations

Triangle ABC is an isosceles triangle

Advertisements

Lesson 9-5 Pages The Pythagorean Theorem Lesson Check 9-4.

Exercise Solve x 2 = 4. x = ± 2. Solve x 2 = – 4. no real solution Exercise.

Section 11-2 The Pythagorean Theorem SPI 32A: apply the Pythagorean Theorem to real life problem illustrated by a diagram Objectives: Solve problems using.

Section 8-2 The Pythagorean Theorem Objectives: Solve problems using the Pythagorean Theorem Right Angle: angle that forms 90° Hypotenuse: in a right triangle,

Then/Now You have already found missing measures of similar triangles. (Lesson 6–7) Use the Pythagorean Theorem to find the length of a side of a right.

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

Aim: How do we find the lengths of the sides in a right triangle? Do Now 1. Solve 2(x + 5) = Find the measure of the missing angle? 48 o 17 o 100.

7B Pythagorean Theorem and Its Converse

The Pythagorean Theorem

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.

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.

Chapter 7.1 & 7.2 Notes: The Pythagorean Theorem and its Converse

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

Geometry Notes Lesson 5.1B Pythagorean Theorem T.2.G.4 Apply the Pythagorean Theorem and its converse in solving practical problems.

Ch 9.1 The Pythagorean Theorem Definition of the Day Right Triangle Legs of a Triangle Hypotenuse of a Triangle The Pythagorean Theorem.

Lesson 10-2 Warm-Up.

9/23/ : The Pythagoream Theorem 5.4: The Pythagorean Theorem Expectation: G1.2.3: Know a proof of the Pythagorean Theorem and use 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.

Holt Course 2 NY-10 Using the Pythagorean Theorem NY-10 Using the Pythagorean Theorem Holt Course 2 Lesson Presentation Lesson Presentation.

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

Prentice Hall Lesson 11.2 EQ: What is the Pythagorean Theorem? BOP:

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

Sec: 7.1 and 7-2 Sol: G.7. Find the geometric mean between each pair of numbers. 4 and 9.

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.

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.

ALGEBRA READINESS LESSON 3-6 Warm Up Lesson 3-6 Warm Up.

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

The Pythagorean Theorem describes the relationship between the length of the hypotenuse c and the lengths of the legs a & b of a right triangle. In a right.

Lesson 11-3 Pages The Pythagorean Theorem.

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.

ALGEBRA READINESS LESSON 3-6 Warm Up Lesson 3-6 Warm Up.

Special Right Triangles

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

Sec: 8.1 Sol: G.8 Theorem 7.4: Pythagorean Theorem In a right triangle the sum of the squares of the measures of the legs equals the square of the measure.

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.

What is a right triangle? A triangle with a right angle.

The Pythagorean Theorem

Section 8-1. Find the geometric mean between each pair of numbers. 4 and 9.

AGENDA LOGIC PUZZLE LESSON 83 CORRECTIONS? WARM-UP L84 QUESTIONS LESSON 85 EXIT CARD.

8-8 The Pythagorean Theorem Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.

10-2 The Pythagorean Theorem Hubarth Algebra. leg hypotenuse Pythagorean Theorem In any right triangle, the sum of the squares of the lengths of the legs.

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.

Main Idea and New Vocabulary Key Concept: Pythagorean Theorem

The Pythagorean Theorem

Find the geometric mean between 9 and 13.

SOL 8.10 Pythagorean Theorem.

Section 11-2 The Pythagorean Theorem SPI 32A: apply the Pythagorean Theorem to real life problem illustrated by a diagram Objectives: Solve problems.

Objective The student will be able to:

The Pythagorean Theorem

Pythagoras’ Theorem – Outcomes

Use your graphing calculator to solve each equation.

The Pythagorean Theorem

Main Idea and New Vocabulary Key Concept: Pythagorean Theorem

Pythagorean Theorem What is it??

6-3 The Pythagorean Theorem Pythagorean Theorem.

5-7 The Pythagorean Theorem

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

The Pythagorean Theorem

5-3: The Pythagorean Theorem

The Pythagorean Theorem and Its Converse

Solve each equation Solve each equation. x2 – 16 = n = 0

Lesson 8-7 The Pythagorean Theorem

If a triangle is a RIGHT TRIANGLE, then a2 + b2 = c2.

The Pythagorean Theorem

The Pythagorean Theorem

Presentation transcript:

Objective The learner will solve problems using the Pythagorean Theorem

WHY? To find missing sides of right triangles & to calculate heights

Lesson 11 – 2 The Pythagorean Theorem Pages

Pythagorean Theorem Pythagoras Pythagorean Theorem Proof

In a right triangle, the side opposite the right angle is the hypotenuse. It is the longest side. Each of the sides forming the right angle is a leg. The Pythagorean Theorem describes the relationship of the lengths of the sides of a right triangle. hypotenuse legs

The Pythagorean Theorem 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 a b c

Example #1 What is the length of the hypotenuse of the triangle? a² + b² = c² 9² + 12² = c² = c² 225 = c² √225 = √c² 15 = cThe hypotenuse is 15cm. 9 cm 12 cm c

Now you try: What is the length of the hypotenuse of a right triangle with legs of lengths 7 cm and 24 cm? You can also use the Pythagorean Theorem to find the length of a leg of a right triangle when you know the length of the hypotenuse and the other leg.

Example #2 A fire truck parks beside a building such that the base of the ladder is 16ft from the building. The fire truck extends its ladder 30ft to reach the top of the building. How high is the top of the ladder above the ground? See work on the board.

Now you try: Use the figure at the right. About how many miles is it from downtown to the harbor? Round to the nearest tenth of a mile. Harbor Downtown Highway 4mi 8mi b

Converse of Pythagorean Theorem If a triangle has sides of lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle with a hypotenuse of length c. You can use the converse of the Pythagorean Theorem to determine whether a triangle is a right triangle.

Example #3 Determine whether the given lengths are sides of a right triangle. a. 5in, 12in, and 13in a² + b² = c² 5² + 12² = 13² = = 169 So the triangle is a right triangle.

Now you try: A triangle has sides of lengths 10m, 24m, and 26m. Is the triangle a right triangle?

Open Book Page 584