9.2 The Pythagorean Theorem

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Presentation transcript:

9.2 The Pythagorean Theorem Unit IIB Day 5

Do Now What is the Pythagorean Theorem? What is the formula for area of a triangle?

History Lesson Around the 6th century BC, the Greek mathematician Pythagoras 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.

Thm 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 legs.

Using the Pythagorean Theorem A Pythagorean triple is a set of three positive integers a, b, and c that satisfy the equation c2 = a2 + b2 For example, the integers 3, 4 and 5 form a Pythagorean Triple because 52 = 32 + 42.

Ex. 1: Finding the length of the hypotenuse. Find the length of the hypotenuse of the right triangle. Tell whether the sides lengths form a Pythagorean Triple. x = 13 Because the side lengths 5, 12 and 13 are integers, they form a Pythagorean Triple.

Ex. 2: Finding the Length of a Leg Find the length of the leg of the right triangle. X = sqrt(147) = 7sqrt(3)

Ex. 3: Area of a triangle Find the area of the triangle to the nearest tenth of a meter. Because the triangle is isosceles, it can be divided into two congruent triangles with the given dimensions. Use the Pythagorean Theorem to find the value of h. √24 = h Area = ½ bh = ½ (10)(√24) = 10√6 ≈ 24.5 m2

Ex. 3a: Area of a triangle Find the area of the triangle to the nearest tenth of a meter. Because the triangle is isosceles, it can be divided into two congruent triangles with the given dimensions. Use the Pythagorean Theorem to find the value of h. √40 = h Area = ½ bh = ½ (10)(√40) ≈ 31.2 m2

Closure Find the length of the second leg of a right triangle with hypotenuse 18 and leg 12. Express your answer to the nearest tenth. 13.4