Lesson 11.4 Apply the Pythagorean Theorem and Its Converse

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Presentation transcript:

Lesson 11.4 Apply the Pythagorean Theorem and Its Converse Essential Question: How do you use the Pythagorean theorem and its converse?

Before we start… What is a right triangle? Draw one. Label the two sides of the triangle that form the right angles as a and b. Label the longest side of the triangle as c. Let 𝑎=3,𝑏=4, 𝑎𝑛𝑑 𝑐=5. Square a and b and find the sum of the squares. Tell how the sum compares to the square of c.

What are the parts of the right triangle? The hypotenuse is the side opposite the right angle. It is the longest side of the right triangle. The legs are the two sides that form the right angle.

What is the Pythagorean theorem? It states the relationship among the lengths of the sides of a right triangle. A theorem is a statement that can be proved true.

What does the Pythagorean theorem say? If a triangle is a right triangle, then the sum of the squares of the lengths of the legs equals the square of the lengths of the hypotenuse. 𝑎 2 + 𝑏 2 = 𝑐 2

Find the unknown length for the triangle shown.

Find the unknown length for the triangle shown.

Find the unknown length for the triangle shown.

Find the unknown length for the triangle shown.

A right triangle has one leg that is 2 inches longer than the other leg. The length of the hypotenuse is 10 inches. Find the unknown lengths.

A right triangle has one leg that is 1 foot longer than the other leg A right triangle has one leg that is 1 foot longer than the other leg. The length of the hypotenuse is 13 feet. Find the unknown lengths.

Find the unknown length for the triangle shown.

Find the unknown length for the triangle shown.

A soccer player makes a corner kick to another player, as shown A soccer player makes a corner kick to another player, as shown. To the nearest yard, how far does the player kick the ball?

What is the Converse of the Pythagorean Theorem? If a triangle has side lengths, a, b and c such that 𝑎 2 + 𝑏 2 = 𝑐 2 , then the triangle is a right triangle.

Tell whether the triangle with the given side lengths is a right triangle. 8, 15, 17

Tell whether the triangle with the given side lengths is a right triangle. 5, 8, 9

Tell whether the triangle with the given side lengths is a right triangle. 7, 23, 24

Tell whether the triangle with the given side lengths is a right triangle. 5, 12, 13

Construction 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?

Window Design 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?

Lot Size A real estate lot is in the shape of a triangle Lot Size A real estate lot is in the shape of a triangle. The side lengths are 48 feet, 55 feet, and 73 feet. The real estate agent told a potential buyer that one of the corners forms a right angle. Is the real estate agent correct?

How do you use the Pythagorean theorem and its converse?