Apply the Pythagorean Theorem and Its Converse

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Presentation transcript:

Apply the Pythagorean Theorem and Its Converse

Lesson Essential Question Create one situation in which the Pythagorean Theorem or its converse is useful?

Terminology Hypotenuse – the side opposite the right angle Pythagorean Theorem – the relationship between the lengths of the sides of a right triangle.

Example 1: Use the Pythagorean Theorem Find the unknown length for the triangles: a, b = 6, c = 7 A= 5, b = 12, c =

Ex 2: Use the Pythagorean Theorem 1) A right triangle has one leg that is 2 inches higher than the other leg. The length of the hypotenuse is √10 inches. Find the unknown lengths. 2) A right triangle has one leg that is 3 inches longer than the other leg. The length of the hypotenuse is 15 inches. Find the unknown lengths.

Ex 2: Continued 3) A right triangle has one leg that is 1 foot higher than the other leg. The length of the hypotenuse is √13 feet. Find the unknown lengths.

Ex 3: Application Problems 1) A soccer player makes a corner kick to another player, as shown. To the nearest yard, how far does the player kick the ball? 2) A rectangular pool is 30 feet wide and 60 feet long. You swim diagonally across the pool. To the nearest foot, how far do you swim?

Ex 4: Determine right triangles Tell whether the triangles with the given side lengths is a right triangle. 1) 8, 15, 7 2) 5, 8, 9 3) 7, 23, 24 4) 5, 12, 13

Ex 5: Use the converse of the Pythagorean Theorem 1) A construction worker is making sure one corner of the foundation of the corner of a house is a right angle. To do this, the worker makes a mark 8 feet from the corner along one wall and another mark 6 feet from the same corner along the other wall. The worker then measures the distance between the two marks and finds the distance to be 10 feet. Is the corner a right angle?

Ex 5: Use the converse of the Pythagorean Theorem 2) A window has the shape of a triangle with the lengths of 120 centimeters, 120 centimeters, and 180 centimeters. Is the window a right triangle? Explain.

Summary Question Create one situation in which the Pythagorean Theorem or its converse is useful? Exchange this problem with a partner. Solve your partner’s problem.