Quote of the Day Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write. -H. G. Wells.

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PYTHAGOREAN THEOREM.

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Presentation transcript:

Quote of the Day Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write. -H. G. Wells

Apply the Pythagorean Theorem and Its Converse Section 11.4

Objectives: Apply the Pythagorean Theorem Apply the converse of the Pythagorean Theorem

Key Vocabulary: Hypotenuse Legs of a right triangle Pythagorean Theorem

Hypotenuse and Legs of a right triangle The hypotenuse of a right triangle is the side opposite the right angle. It is the longest side of a right triangle. The legs are the two sides that form the right angle.

The Pythagorean Theorem

Example 1: Find the unknown length for the triangle shown.

#1: Find the value of c.

Example 2: A right triangle has one leg that is 2 inches longer than the other leg. The length of the hypotenuse is inches. Find the unknown lengths.

Example 3:

#2: Complete. A right triangle ahs one leg that is 3 inches longer than the other leg. The length of the hypotenuse is 15 inches. Find the unknown lengths.

#3: Complete. 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?

Converse of the Pythagorean Theorem

Example 4: Tell whether the triangle with the given side lengths is a right triangle. 8, 15, 17 5, 8, 9

Example 5: A construction worker is making sure one corner of the foundation 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?

#4: Tell whether the triangle with the given side lengths is a right triangle. 7, 11, 13

#5: Tell whether the triangle with the given side lengths is a right triangle. 15, 36, 39

#6: Tell whether the triangle with the given side lengths is a right triangle. 15, 112, 113

#7: Complete. A window has the shape of a triangle with side lengths of 120 centimeters, 120 centimeters, and 180 centimeters. Is the window a right triangle?

Partner Work Page 740 #4, 14, 16, 17, 21, 25, 27

Homework Assignment Page 740 #6, 8, 10, 12, 18, 20, 22, 24, 26, 28, 34, 36, 38