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9.2 The Pythagorean Theorem

9.2 The Pythagorean Theorem. Geometry. Objectives/Assignment. Use the Pythagorean Theorem Use the Pythagorean Theorem to solve real-life problems such as determining how far a ladder will reach. History Lesson.

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9.2 The Pythagorean Theorem

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  1. 9.2 The Pythagorean Theorem Geometry

  2. Objectives/Assignment • Use the Pythagorean Theorem • Use the Pythagorean Theorem to solve real-life problems such as determining how far a ladder will reach.

  3. History Lesson • Around the 6th century BC, the Greek mathematician Pythagorus founded a school for the study of philosophy, mathematics and science. Many people believe that an early proof of the Pythagorean Theorem came from this school. • Today, the Pythagorean Theorem is one of the most famous theorems in geometry. Over 100 different proofs now exist.

  4. In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the legs. Theorem 9.4: Pythagorean Theorem c2 = a2 + b2

  5. Using the Pythagorean Theorem • A Pythagorean triple is a set of three positive integers a, b, and c that satisfy the equation c2 = a2 + b2For example, the integers 3, 4 and 5 form a Pythagorean Triple because 52 = 32 + 42.

  6. Find the length of the hypotenuse of the right triangle. Tell whether the sides lengths form a Pythagorean Triple. Ex. 1: Finding the length of the hypotenuse.

  7. Find the length of the leg of the right triangle. Ex. 2: Finding the Length of a Leg

  8. Find the area of the triangle to the nearest tenth of a meter. You are given that the base of the triangle is 10 meters, but you do not know the height. Ex. 3: Finding the area of a triangle

  9. Area of a Triangle Area = ½ bh = ½ (10)(√24) ≈ 24.5 m2 The area of the triangle is about 24.5 m2

  10. Support Beam: The skyscrapers shown on page are connected by a skywalk with support beams. You can use the Pythagorean Theorem to find the approximate length of each support beam. Ex. 4: Indirect Measurement

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