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 ( 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 = c = c = 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 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 b 2 = 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 = c = 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 = c = 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 + b Triangle is acute c 2 > a 2 + b Triangle is obtuse c2 = a2 + b 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 = ? 100 = ?
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 = ? 256 = ?