Objective The student will be able to:

Slides:

Advertisements

Similar presentations

Created by G. Antidormi 2003 The Pythagorean Theorem.

Advertisements

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. 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’

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

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.

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

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

Find square roots. Find cube roots. 7.1 Objective The student will be able to:

Objective The student will be able to:

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

Course The Pythagorean Theorem OBJECTIVE January 23, 2014 In our study of THE PYTHAGOREAN THEORM (Readiness) the students will be able to Calculate.

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

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

Objective The student will be able to: use the Pythagorean Theorem.

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

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.

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

¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓÃ£ÖÖ,ÃÖÖ ŸÖÖ¸üÖ ú´ÖÔ¾Öß¸ü ×¾ÖªÖ¯ÖÏ²ÖÖê× ¬ÖÖß, ´Ö¬µÖ ×¾Ö³ÖÖÖ, ÃÖÖŸÖÖ¸üÖ ¿ÖÖ»ÖêµÖ †³µÖÖÃÖÎú´ÖÖÖãÃÖÖ¸ ÃÖÓÃ£ÖêŸÖß»Ö ÃÖê¾ÖúÖÓÖß ŸÖµÖÖ¸ü.

 Remember the pattern for right triangles: Area of small square + Area of medium square = Area of large square.

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.

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

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.

Pythagorean Theorem Distance Formula. Vocabulary Right Triangle – A Triangle with one 90° angle Hypotenuse – The longest side of a right triangle (opposite.

The Pythagorean Theorem

The Distance and Midpoint Formulas

The Right Triangle and The Pythagorean Theorem

SOL 8.10 Pythagorean Theorem.

Objective The student will be able to:

Pythagorean Theorem CC A.3 - Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real- world and mathematical problems.

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

12-2 The Pythagorean Theorem

Objective The student will be able to:

Pythagorean Theorem What is it??

6.2: Pythagorean Theorem Objectives:

Objective- To solve problems involving the Pythagorean Theorem.

6-3 The Pythagorean Theorem Pythagorean Theorem.

Pythagorean Theorem.

Pythagorean Theorem.

5-7 The Pythagorean Theorem

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

5-3: The Pythagorean Theorem

PYTHAGORAS Born c. 570 BC Samos Died

7.0: Pythagorean Theorem Objectives:

The Pythagorean Theorem

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

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

Right Triangles Unit 4 Vocabulary.

Objective- To solve problems involving the Pythagorean Theorem.

G3.2 Pythagorean Theorem Objectives:

Objective The student will be able to:

6.5 Pythagorean Theorem.

Objective Students will be able to:

Objective The student will be able to:

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

Pythagorean Theorem, its Converse and the coordinate system

Objective The student will be able to:

Objective The student will be able to:

Objective The student will be able to:

Objective The student will be able to:

The Pythagorean Theorem

Pythagorean Theorem GOAL: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in.

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

Proving Right Triangles

Presentation transcript:

Objective The student will be able to: use the Pythagorean Theorem SOL: A.13 Designed by Skip Tyler, Varina High School

What is a right triangle? hypotenuse leg right angle leg 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 opposite the right angle is the hypotenuse.

The Pythagorean Theorem In a right triangle, if a and b are the measures of the legs and c is the hypotenuse, then a2 + b2 = c2. Note: The hypotenuse, c, is always the longest side.

Find the length of the hypotenuse if 1. a = 12 and b = 16. 122 + 162 = c2 144 + 256 = c2 400 = c2 Take the square root of both sides. 20 = c

Find the length of the hypotenuse if 2. a = 5 and b = 7. 52 + 72 = c2 25 + 49 = c2 74 = c2 Take the square root of both sides. 8.60 = c

Take the square root of both sides. Find the length of the leg, to the nearest hundredth, if 3. a = 4 and c = 10. 42 + b2 = 102 16 + b2 = 100 Solve for b. 16 - 16 + b2 = 100 - 16 b2 = 84 Take the square root of both sides. b = 9.17

Take the square root of both sides. Find the length of the leg, to the nearest hundredth, if 4. c = 10 and b = 7. a2 + 72 = 102 a2 + 49 = 100 Solve for a. a2 = 100 - 49 a2 = 51 Take the square root of both sides. a = 7.14

5. The measures of three sides of a triangle are given below 5. The measures of three sides of a triangle are given below. Determine whether each triangle is a right triangle. , 3, and 8 Which side is the biggest? The square root of 73 (= 8.5)! This must be the hypotenuse (c). Plug your information into the Pythagorean Theorem. It doesn’t matter which number is a or b.

Sides: , 3, and 8 32 + 82 = ( ) 2 9 + 64 = 73 73 = 73 Since this is true, the triangle is a right triangle!! If it was not true, it would not be a right triangle.