# aselhajj1 Pythagoras (580 - 500 B.C.) He was a Greek philosopher responsible for important developments in mathematics, astronomy and the theory of music.

## Presentation on theme: "aselhajj1 Pythagoras (580 - 500 B.C.) He was a Greek philosopher responsible for important developments in mathematics, astronomy and the theory of music."— Presentation transcript:

aselhajj1 Pythagoras (580 - 500 B.C.) He was a Greek philosopher responsible for important developments in mathematics, astronomy and the theory of music.

aselhajj2 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... a 2 + b 2 = c 2 The hypotenuse is the side that faces the right angle and its always the longest hypotenuse (c) leg (a) leg (b) The Pythagorean Theorem

aselhajj3 What is the length of the hypotenuse ? Step 1. Write the formula for the Pythagorean Theorem. Step 2. Substitute in known values. Step 3. Solve for the unknown variable. a 2 + b 2 = c 2 8 2 + 15 2 = c 2 64 + 225 = c 2 289 = c 2 The Pythagorean Theorem

aselhajj4 A television screen measures approximately 15.5 in. high and 19.5 in. wide. A television is advertised by giving the approximate length of the diagonal of its screen. How should this television be advertised? Draw and label a diagram to model the problem. 15.5 19.5 c Solve for c, using the Pythagorean Theorem. The television should be advertised as a 25.

aselhajj5 Ladder Problem A ladder leans against a second-story window of a house. If the ladder is 25 meters long, and the base of the ladder is 7 meters from the house, how high is the window?

aselhajj6 Distance from house: 7 meters First draw a diagram that shows the right triangle. Label the sides: –Ladder is 25 m –Distance from house is 7 m Use Pythagorean theorem a 2 + b 2 = c 2 to solve Ladder Problem 7 2 + b 2 = 25 2 49 + b 2 = 625 b 2 = 576 b = 24

aselhajj7 A set of three whole numbers a, b, and c such that a 2 + b 2 = c 2 is called a Pythagorean triple. Pythagorean Triples

aselhajj8 Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain. Since the side lengths are whole numbers that satisfy the equation a 2 + b 2 = c 2, so they form a Pythagorean triple. a 2 + b 2 = c 2 14 2 + 48 2 = c 2 2500 = c 2 50 = c 14 48

aselhajj9 Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain. a 2 + b 2 = c 2 8 2 + 10 2 = c 2 164 = c 2 The side lengths do not form a Pythagorean triple because is not a whole number. 8 10

aselhajj10 You can also use Pythagorean theorem to classify a triangle as acute or obtuse. Pythagorean Inequalities: c2 < a2 + b2 - - - Triangle is acute c 2 > a 2 + b 2 - - - Triangle is obtuse c2 = a2 + b2 - - - Triangle is Right

aselhajj11 Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right. 5, 7, 10 Since c 2 > a 2 + b 2, the triangle is obtuse. 100 > 74 c 2 = a 2 + b 2 ? 10 2 = 5 2 + 7 2 ? 100 = 25 + 49 ?

aselhajj12 7, 12, 16 Since c 2 > a 2 + b 2, the triangle is obtuse. 256 > 193 c 2 = a 2 + b 2 ? 16 2 = 12 2 + 7 2 ? 256 = 144 + 49 ?

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The content structure consists of a series of slides about Pythagoras and the Pythagorean Theorem, including examples and problems that apply the theorem.
multiple_questions_with_answers

the passage contains multiple mathematical questions and their corresponding answers, all related to the pythagorean theorem. specifically:
- slide 3 provides a step-by-step solution to find the hypotenuse of a right triangle with legs 8 and 15.
- slide 4 solves for the diagonal of a television screen using the pythagorean theorem.
- slide 6 solves the ladder problem to find the height of a window.
- slide 8 and 9 find missing side lengths and determine if they form pythagorean triples.
- slide 11 and 12 classify triangles as acute, obtuse, or right using the pythagorean inequalities.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# aselhajj1 Pythagoras (580 - 500 B.C.) He was a Greek philosopher responsible for important developments in mathematics, astronomy and the theory of music.

## Presentation on theme: "aselhajj1 Pythagoras (580 - 500 B.C.) He was a Greek philosopher responsible for important developments in mathematics, astronomy and the theory of music."— Presentation transcript:

aselhajj1 Pythagoras (580 - 500 B.C.) He was a Greek philosopher responsible for important developments in mathematics, astronomy and the theory of music.

aselhajj2 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... a 2 + b 2 = c 2 The hypotenuse is the side that faces the right angle and its always the longest hypotenuse (c) leg (a) leg (b) The Pythagorean Theorem

aselhajj3 What is the length of the hypotenuse ? Step 1. Write the formula for the Pythagorean Theorem. Step 2. Substitute in known values. Step 3. Solve for the unknown variable. a 2 + b 2 = c 2 8 2 + 15 2 = c 2 64 + 225 = c 2 289 = c 2 The Pythagorean Theorem

aselhajj4 A television screen measures approximately 15.5 in. high and 19.5 in. wide. A television is advertised by giving the approximate length of the diagonal of its screen. How should this television be advertised? Draw and label a diagram to model the problem. 15.5 19.5 c Solve for c, using the Pythagorean Theorem. The television should be advertised as a 25.

aselhajj5 Ladder Problem A ladder leans against a second-story window of a house. If the ladder is 25 meters long, and the base of the ladder is 7 meters from the house, how high is the window?

aselhajj6 Distance from house: 7 meters First draw a diagram that shows the right triangle. Label the sides: –Ladder is 25 m –Distance from house is 7 m Use Pythagorean theorem a 2 + b 2 = c 2 to solve Ladder Problem 7 2 + b 2 = 25 2 49 + b 2 = 625 b 2 = 576 b = 24

aselhajj7 A set of three whole numbers a, b, and c such that a 2 + b 2 = c 2 is called a Pythagorean triple. Pythagorean Triples

aselhajj8 Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain. Since the side lengths are whole numbers that satisfy the equation a 2 + b 2 = c 2, so they form a Pythagorean triple. a 2 + b 2 = c 2 14 2 + 48 2 = c 2 2500 = c 2 50 = c 14 48

aselhajj9 Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain. a 2 + b 2 = c 2 8 2 + 10 2 = c 2 164 = c 2 The side lengths do not form a Pythagorean triple because is not a whole number. 8 10

aselhajj10 You can also use Pythagorean theorem to classify a triangle as acute or obtuse. Pythagorean Inequalities: c2 < a2 + b2 - - - Triangle is acute c 2 > a 2 + b 2 - - - Triangle is obtuse c2 = a2 + b2 - - - Triangle is Right

aselhajj11 Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right. 5, 7, 10 Since c 2 > a 2 + b 2, the triangle is obtuse. 100 > 74 c 2 = a 2 + b 2 ? 10 2 = 5 2 + 7 2 ? 100 = 25 + 49 ?

aselhajj12 7, 12, 16 Since c 2 > a 2 + b 2, the triangle is obtuse. 256 > 193 c 2 = a 2 + b 2 ? 16 2 = 12 2 + 7 2 ? 256 = 144 + 49 ?

Download ppt "aselhajj1 Pythagoras (580 - 500 B.C.) He was a Greek philosopher responsible for important developments in mathematics, astronomy and the theory of music."

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user
The content structure consists of a series of slides about Pythagoras and the Pythagorean Theorem, including examples and problems that apply the theorem.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS

The passage contains multiple mathematical questions and their corresponding answers, all related to the Pythagorean Theorem. Specifically:
- Slide 3 provides a step-by-step solution to find the hypotenuse of a right triangle with legs 8 and 15.
- Slide 4 solves for the diagonal of a television screen using the Pythagorean Theorem.
- Slide 6 solves the ladder problem to find the height of a window.
- Slide 8 and 9 find missing side lengths and determine if they form Pythagorean triples.
- Slide 11 and 12 classify triangles as acute, obtuse, or right using the Pythagorean inequalities.