Apply the Pythagorean Theorem Chapter 7.1. Sides of a Right Triangle Hypotenuse – the side of a right triangle opposite the right angle and the longest.

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Presentation transcript:

Apply the Pythagorean Theorem Chapter 7.1

Sides of a Right Triangle Hypotenuse – the side of a right triangle opposite the right angle and the longest side. Legs – the sides of a right triangle that are not the hypotenuse.

The 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.

Proving the Pythagorean Theorem There are multiple ways of proving the Pythagorean Theorem. If you can find a legitimate proof of the Pythagorean theorem you may earn 2 bonus points.

Using the Pythagorean Theorem 68x²x² = x ² 100= x ²

Find the missing leg x3 5² x ² + 9 = 25 x ² = 16

Find the Area of the Triangle What is the formula for the area of a triangle? A = ½bh How will we find the height?

Find the Area of the Triangle

Pythagorean Triples A Pythagorean Triple is a set of 3 positive integers or whole numbers that satisfies the Pythagorean theorem.

Is it a Pythagorean Triple? 3, 4, and 5 21, 28, and 35 30, 72, and 91 14, 48, and 50 yes no yes

If I am given 2 sides of a right triangle make up the sides of Pythagorean triple, how do you find the missing side? There are 2 possible scenarios: 1.You are given both legs of the right triangle and need to solve for the hypotenuse. 2.You are given one leg and one hypotenuse and need to solve for the other leg.

Given 2 sides: 20 and 25 Scenario and 25 are the legs = x = x = x = x This cannot be the answer for a Pythagorean triple because it is not a whole number. Scenario and 25 are the leg and hypotenuse x 2 = x 2 = 625 x 2 = 225 X = 25 This can be the answer for a Pythagorean triple because it is not a whole number.

Given 2 sides: 28 and 96

Find the area when given a leg and the hypotenuse 1.Find the other leg by plugging the known values into the Pythagorean Theorem. 2.Use the 2 legs in the formula for area of a triangle  A = ½BH

Find the area when given a leg and a hypotenuse. L=8 and h= 16 A ò+8ò=16ò A ò+64=256 A ò=192

Find the area when given a leg and a hypotenuse. L=13 and h= 17 A ò+13ò=17ò A ò+169=289 A ò=120

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