Remember Rough Draft is due Quiz Corrections are due

Slides:



Advertisements
Similar presentations
GOAL 1 PROPORTIONS IN RIGHT TRIANGLES EXAMPLE Similar Right Triangles THEOREM 9.1 If the altitude is drawn to the hypotenuse of a right triangle,
Advertisements

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
9.2 The Pythagorean Theorem Geometry Mrs. Spitz Spring 2005.
EXAMPLE 2 Standardized Test Practice SOLUTION =+.
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.
EXAMPLE 2 Standardized Test Practice SOLUTION =+.
12.3 The Pythagorean Theorem CORD Mrs. Spitz Spring 2007.
7.1 The Pythagorean Theorem
9.2 The Pythagorean Theorem
The Pythagorean Theorem
Objectives Use the Pythagorean Theorem and its converse to solve problems. Use Pythagorean inequalities to classify triangles.
Benchmark 40 I can find the missing side of a right triangle using the Pythagorean Theorem.
Chapter 7.1 & 7.2 Notes: The Pythagorean Theorem and its Converse
Pythagorean Theorem 5.4. Learn the Pythagorean Theorem. Define Pythagorean triple. Learn the Pythagorean Inequality. Solve problems with the Pythagorean.
Pythagorean Theorem Use the Pythagorean Theorem to find the missing length of the right triangle. 1.
Apply the Pythagorean Theorem
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:
Section 7.1 – Solving Quadratic Equations. We already know how to solve quadratic equations. What if we can’t factor? Maybe we can use the Square Root.
9.2 The Pythagorean Theorem Geometry Mrs. Gibson Spring 2011.
1. Solve x2 = 100. ANSWER 10, –10 2. Solve x2 + 9 = 25. ANSWER 4, –4
Geometry The function of education is to teach one to think intensively and to think critically. Intelligence plus character - that is the goal of true.
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.
Unit 6 Lesson 1 The Pythagorean Theorem
Warm-Up Exercises 2. Solve x = 25. ANSWER 10, –10 ANSWER 4, –4 1. Solve x 2 = 100. ANSWER Simplify 20.
Objectives: 1) To use the Pythagorean Theorem. 2) To use the converse of the Pythagorean Theorem.
9.2 The Pythagorean Theorem
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.
Sec. 8-1 The Pythagorean Theorem and its Converse.
SOLUTION Finding Perimeter and Area STEP 1 Find the perimeter and area of the triangle. Find the height of the triangle. Pythagorean Theorem Evaluate powers.
Chapter 7 Right Triangles and Trigonometry Objectives: Use calculator to find trigonometric ratios Solve for missing parts of right triangles.
8.1 Pythagorean Theorem Understand how to use the Pythagorean Theorem and its converse to solve problems Do Now: 1. An entertainment center is 52 in. wide.
Guided Notes/Practice
Main Idea and New Vocabulary Key Concept: Pythagorean Theorem
Warm Up Simplify the square roots
Pythagorean theorem.
1. Solve x2 = 100. ANSWER 10, –10 2. Solve x2 + 9 = 25. ANSWER 4, –4
Right Triangle The sides that form the right angle are called the legs. The side opposite the right angle is called the hypotenuse.
Pythagorean Theorem and Its Converse
9.2 The Pythagorean Theorem
7.1 Apply the Pythagorean Theorem
The Pythagorean Theorem
7.2 The Pythagorean Theorem and its Converse
Section 1 – Apply the Pythagorean Theorem
Chapter 9 Right Triangles and Trigonometry
Chapter 9 Right Triangles and Trigonometry
Objectives Use the Pythagorean Theorem and its converse to solve problems. Use Pythagorean inequalities to classify triangles.
9.2 The Pythagorean Theorem
9-2 Pythagorean Theorem.
The Pythagorean Theorem is probably the most famous mathematical relationship. As you learned in Lesson 1-6, it states that in a right triangle, the sum.
Chapter 10 Section 10.1 Pythagorean Theorem.
Main Idea and New Vocabulary Key Concept: Pythagorean Theorem
Quiz Review.
The Pythagorean Theorem
PROVING THE PYTHAGOREAN THEOREM
Objectives/Assignment
10.3 and 10.4 Pythagorean Theorem
7-1 and 7-2: Apply the Pythagorean Theorem
7.1 Apply the Pythagorean theorem.
11.7 and 11.8 Pythagorean Thm..
The Pythagorean Theorem
9.2 The Pythagorean Theorem
1. Solve x2 = 100. ANSWER 10, –10 2. Solve x2 + 9 = 25. ANSWER 4, –4
Right Triangles and Trigonometry
Presentation transcript:

Remember Rough Draft is due Quiz Corrections are due Make sure that you have your stuff Calculator Sharpened Pencil Ruler Protractor

Chapter 9 Right Triangles and Trigonometry Section 9.2 Pythagorean Theorem PROVE THE PYTHAGOREAN THEOREM USE THE PYTHAGOREAN THEOREM

The Pythagorean Theorem In a Right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse.

PROVING THE PYTHAGOREAN THEOREM THEOREM 9.4 Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. b a c c 2 = a 2 + b 2

USE THE PYTHAGOREAN THEOREM True True False False True True

Pythagorean Triples If the sides of a Right triangle are integers, then the sides are known as a Pythagorean Triple 7, 24, 25 Do you know any other ?

USING THE PYTHAGOREAN THEOREM A Pythagorean triple is a set of three positive integers a, b, and c that satisfy the equation c 2 = a 2 + b 2. For example, the integers 3, 4, and 5 form a Pythagorean triple because 5 2 = 32 + 4 2.

(hypotenuse)2 = (leg)2 + (leg)2 Finding the Length of a Hypotenuse 12 x 5 Find the length of the hypotenuse of the right triangle. Tell whether the side lengths form a Pythagorean triple. SOLUTION (hypotenuse)2 = (leg)2 + (leg)2 Pythagorean Theorem x 2 = 5 2 + 12 2 Substitute. x 2 = 25 + 144 Multiply. x 2 = 169 Add. x = 13 Find the positive square root. Because the side lengths 5, 12, and 13 are integers, they form a Pythagorean triple.

(hypotenuse)2 = (leg)2 + (leg)2 Finding the Length of a Leg Many right triangles have side lengths that do not form a Pythagorean triple. x 14 7 Find the length of the leg of the right triangle. SOLUTION (hypotenuse)2 = (leg)2 + (leg)2 Pythagorean Theorem 14 2 = 7 2 + x 2 Substitute. 196 = 49 + x 2 Multiply. 147 = x 2 Subtract 49 from each side. 147 = x Find the positive square root. 49 • 3 = x Use product property. 7 3 = x Simplify the radical.

Yes 5, 12, 13 is a Pythagorean triple Finding the Missing Length SOLUTION (hypotenuse)2 = (leg)2 + (leg)2 Pythagorean Theorem 13 2 = 12 2 + x 2 Substitute. 169 = 144 + x 2 Multiply. 25 = x 2 Subtract 144 from each side. 25 = x Find the positive square root. 5= x Simplify the radical. Yes 5, 12, 13 is a Pythagorean triple

Area and the Right Triangle Area equals ½ altitude times base A=½ab b and a are the same as the legs of a Right triangle.

2 poles are supported by 100ft cables 50 ft from the ground How far are the poles apart?

Indirect Measurement Closure Question SUPPORT BEAM These skyscrapers are connected by a skywalk with support beams. You can use the Pythagorean Theorem to find the approximate length of each support beam.

Closure Question x 2 = (23.26)2 + (47.57)2 x = (23.26)2 + (47.57)2 Indirect Measurement Closure Question 23.26 m 47.57 m x support beams Each support beam forms the hypotenuse of a right triangle. The right triangles are congruent, so the support beams are the same length. x 2 = (23.26)2 + (47.57)2 Pythagorean Theorem x = (23.26)2 + (47.57)2 Find the positive square root. x  52.95 Use a calculator to approximate. The length of each support beam is about 52.95 meters.

HW Multi-Step Pythagorean Theorem Handout