Bell Work: Use the difference of two squares theorem to write the answers to the following equation. w = 14 2.

Slides:

Advertisements

Similar presentations

Agenda 1) Bell Work 2) Outcomes 3) Review/Finish 8.6 Notes

Advertisements

Quiz Topics Friday’s Quiz will cover: 1) Proportions(parallel lines and angle bisectors of triangles) 2) Pythagorean Theorem 3) Special Right Triangles.

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.

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.

Pythagorean Triples In addition to level 3.0 and beyond what was taught in class, the student may:  Make connection with other concepts in math.

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.

Bell Work: A number cube is rolled once. What is the probability of rolling an even number? Express the probability as a fraction and as a decimal.

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.

Special Right Triangles

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 Eman Almasruhi 3/1/2015. Objectives : Students will know the right triangle. Recognize Pythagorean Theorem. Do some example to show.

4.4: THE PYTHAGOREAN THEOREM AND DISTANCE FORMULA

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

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.

8.1 Pythagorean Theorem and Its Converse

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.

Objective: To use the Pythagorean Theorem and its converse.

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.

Pythagorean Theorum Adham Jad. What is a triangle? How many sides does a triangle have? What is the sum of angles in a triangle? Background & Concept.

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.

Objective The student will be able to:

Learning Outcome: Discover a relationship among the side lengths of a right triangle.

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.

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.

Right Triangles and Trigonometry Chapter Geometric Mean  Geometric mean: Ex: Find the geometric mean between 5 and 45 Ex: Find the geometric mean.

Sullivan Algebra and Trigonometry: Section R.3 Geometry Review Objectives of this Section Use the Pythagorean Theorem and Its Converse Know Geometry Formulas.

College Algebra Section R.3 Geometry Review Objectives of this Section Use the Pythagorean Theorem and Its Converse Know Geometry Formulas.

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

Pythagorean Theorem – Prove It! Converse of Pythagorean Theorem 1.) Is a triangle with side measures of 30, 40, and 50 units a right triangle? Prove it!

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.

Right Triangles A triangle is the simplest polygon in a plane, consisting of three line segments There are many uses of the triangle, especially in construction.

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

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.

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.

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

LESSON 39: DIFFERENCE OF TWO SQUARES, PARALLELOGRAM PROOF, RHOMBUS.

Do Now 5/11/10 Copy HW in your planner. Copy HW in your planner. –Text p. 740, #4-22 evens, #34 In your notebooks, simplify the following expressions.

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.

8.1 Pythagorean Theorem and Its Converse

The Pythagorean Theorem

Pythagorean Triples.

Pythagorean Theorem and it’s Converse

Right Triangle The sides that form the right angle are called the legs. The side opposite the right angle is called the hypotenuse.

The Pythagorean Theorem

Pythagorean Theorem and Its Converse

Pythagorean Theorem and Distance

7.1 Apply the Pythagorean Theorem

Math 3-4: The Pythagorean Theorem

9-2 Pythagorean Theorem.

PYTHAGOREAN THEOREM VOCABULARY.

8-2 The Pythagorean Theorem and Its Converse

8.1 Pythagorean Theorem and Its Converse

5-7 The Pythagorean Theorem

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

5-3: The Pythagorean Theorem

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

8.1 Pythagorean Theorem and Its Converse

PYTHAGOREAN THEOREM VOCABULARY.

6.5 Pythagorean Theorem.

Solve for the unknown side or angle x

Objective: To use the Pythagorean Theorem and its converse.

The Pythagorean Theorem

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.

Right Triangles TC2MA234.

10-1 The Pythagorean Theorem

Presentation transcript:

Bell Work: Use the difference of two squares theorem to write the answers to the following equation. w = 14 2

Answer: ±√14

Lesson 97: Angles and Triangles, Pythagorean Theorem, Pythagorean Triples

Two intersecting lines form four angles. Here are shown two intersecting lines and the four angles they formed.

An angle is formed by two half lines or rays that are in the same plane and that have a common endpoint.

To begin a quick review of angle measures, we remember that if two straight lines intersect and are perpendicular to one another, we define the measure of each of the four angles created to be 90 degrees.

It can be proved, by using geometry, that the sum of the interior angles of any triangle is 180°. We show three triangles and notes that the sum of the three interior angles in each triangle is 180°.

Any triangle that contains a right angle is called a right triangle, and the side of the triangle that is opposite the right angle is always the longest side. We call this side of a right triangle the hypotenuse. The other two sides are called legs, or simply sides.

It can be shown that the square drawn on the hypotenuse of a right triangle has the same area as the sum of the areas of the squares drawn on the other two sides. This idea is known as the Pythagorean theorem.

The general algebraic expression of the Pythagorean Theorem is a + b = c Where c is the length of the hypotenuse and a and b represent the lengths of the other two sides (legs)

Example: Given the triangle with the lengths of the sides as shown, use the Pythagorean theorem to find a. 5 4 a

Answer: a = 3

Example: Find side m. 12 m 8

Answer: m = 4√13

Example: Find k. k √61 5

Answer: k = 6

Pythagorean Triples: It is useful to commit to memory the lengths of the sides of certain right triangles. We show some of these right triangles below.

Note that all the sides of the right triangles show are integers. The triplets of numbers describing the lengths of the three sides of right triangles whose sides are integer lengths are called Pythagorean triples.

It is useful to know that any multiple of a Pythagorean triple is also a Pythagorean triple. For example, a right triangle, right triangle, and right triangle are all Pythagorean triples.

Example: Recall the appropriate Pythagorean triple to find the unknown length in each of the following right triangles. a c b

Answer: a = 13 b = 15 c = 6

HW: Lesson 97 #1-30