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.

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)

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.

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.

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

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’

Geometry Section 9.4 Special Right Triangle Formulas

1 9.1 and 9.2 The Pythagorean Theorem. 2 A B C Given any right triangle, A 2 + B 2 = C 2.

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.

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

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.

Geometry 4.4 SWLT: Use the Pythagorean Theorem to find side lengths of Right Triangles.

12.3 The Pythagorean Theorem

Objective The student will be able to:

Geometry Section 7.4 Special Right Triangles. 45°-45°-90° Triangle Formed by cutting a square in half. n n.

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle.

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.

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.

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

11.4 Pythagorean Theorem Definitions Pythagorean Theorem

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

Honors Geometry Section 5.5 Special Right Triangle Formulas.

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.

How can you prove the Pythagorean Theorem by using the diagram below?

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.

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.

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.

Objective The student will be able to:

The Pythagorean Theorem

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

12-2 The Pythagorean Theorem

The Pythagorean Theorem

Notes Over Pythagorean Theorem

11.4 Pythagorean Theorem.

6-3 The Pythagorean Theorem Pythagorean Theorem.

The Pythagorean Theorem

Special Right Triangles

The Pythagorean Theorem

5-7 The Pythagorean Theorem

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

5-3: The Pythagorean Theorem

7.0: Pythagorean Theorem Objectives:

The Pythagorean Theorem

Pythagorean Theorem a²+ b²=c².

6.5 Pythagorean Theorem.

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

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

The Pythagorean Theorem

10-1 The Pythagorean Theorem

Triangle Relationships

7-2 PYTHAGOREAN THEOREM AND ITS CONVERSE

The Pythagorean Theorem a2 + b2 = c2

Presentation transcript:

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 is the length of the hypotenuse of the right triangle shown.

What is the length of the hypotenuse of a right triangle with les of lengths 9cm and 12cm?

Problem 2: Finding the Length of a Leg What is the side length b in the triangle provided?

Problem 2: Finding the Length of a Leg What is the side length a in the triangle provided?

Problem 3: Identifying Right Triangles Which set of lengths could be the side lengths of a right triangle?