8-8 The Pythagorean Theorem Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

4 5 9 Course The Pythagorean Theorem √18 √26 √86 4. √ Warm Up Estimate each square root to the nearest whole number. Use a calculator to check the reasonableness of your answers

Problem of the Day A shipping carton measures 12 in. by 15 in. by 16 in. What is the longest rod that can be shipped in it? 25 in. Course The Pythagorean Theorem

Learn to use the Pythagorean Theorem to find the measure of a side of a right triangle. Course The Pythagorean Theorem

Vocabulary leg hypotenuse Pythagorean Theorem Insert Lesson Title Here Course The Pythagorean Theorem

Course The Pythagorean Theorem Hypotenuse Leg In a right triangle, the two sides that form the right angle are called legs. The side opposite the right angle is called the hypotenuse. One of the first people to recognize the relationship between the sides of a right triangle was the Greek mathematician Pythagoras. This special relationship is called the Pythagorean Theorem.

Course The Pythagorean Theorem PYTHAGOREAN THEOREM In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. a 2 + b 2 = c 2 a b c

Use the Pythagorean Theorem to find the missing measure. Additional Example 1A: Calculating the Length of a Side of a Right Triangle Course The Pythagorean Theorem A. 12 cm 16 cm a 2 + b 2 = c 2 c = c = c = c 2 The length of the hypotenuse is 20 cm. Use the Pythagorean Theorem. Substitute for a and b. Evaluate the powers. Add. Take the square root of both sides. 20 = c √ 400 = √ c 2

Additional Example 1B: Calculating the Length of a Missing Side of a Right Triangle Course The Pythagorean Theorem Use the Pythagorean Theorem to find the missing measure. B. 5 cm b a 2 + b 2 = c 2 13 cm b 2 = b 2 = 169 b 2 = 144 The length of the missing leg is 12 cm. Use the Pythagorean Theorem. Substitute for a and c. Evaluate the powers. Take the square root of both sides. b = 12 –25 Subtract 25 from each side. √ b 2 = √ 144

Use the Pythagorean Theorem to find the missing measure. Course The Pythagorean Theorem A. 11 cm 15 cm a 2 + b 2 = c 2 c = c = c = c 2 The length of the hypotenuse is about 18.6 cm. Use the Pythagorean Theorem. Substitute for a and b. Evaluate the powers. Add. Take the square root of both sides  c Try This: Example 1A √ 346 = √ c 2

Course The Pythagorean Theorem Use the Pythagorean Theorem to find the missing measure. B. 3 cm b a 2 + b 2 = c 2 5 cm b 2 = b 2 = 25 b 2 = 16 The length of the missing leg is 4 cm. Use the Pythagorean Theorem. Substitute for a and c. Evaluate the powers. Take the square root of both sides. b = 4 –9 Subtract 9 from each side. Try This: Example 1B √ b 2 = √ 16

Course The Pythagorean Theorem Additional Example 2: Problem Solving Application A square field has sides of 75 feet. About how far is it from one corner of the field to the opposite corner of the field? Round your answer to the nearest tenth. 1 Understand the Problem Rewrite the question as a statement. Find the distance from one corner of the field to the opposite corner of the field.

Additional Example 2 Continued Course The Pythagorean Theorem The segment between the two corners is the hypotenuse. The sides of the field are legs, and they are each 75 feet long. 2 Make a Plan You can use the Pythagorean Theorem to write an equation. List the important information: Drawing a segment from one corner of the field to the opposite corner of the field divides the field into two right triangles.

Additional Example 2 Continued Course The Pythagorean Theorem Solve 3 a 2 + b 2 = c = c 2 5, ,625 = c 2 11,250 = c  c The distance from one corner of the field to the opposite corner is about feet Use the Pythagorean Theorem. Substitute for the known variables. Evaluate the powers. Add. Take the square roots of both sides  c Round.

Additional Example 2 Continued Course The Pythagorean Theorem Look Back 4 The hypotenuse is the longest side of a right triangle. Since the distance from one corner of the field to the opposite corner is greater than the length of a side of the field, the answer is reasonable.

Try This: Example 2 Insert Lesson Title Here Course The Pythagorean Theorem A rectangular field has a length of 100 yards and a width of 33 yards. About how far is it from one corner of the field to the opposite corner of the field? Round your answer to the nearest tenth. 1 Understand the Problem Rewrite the question as a statement. Find the distance from one corner of the field to the opposite corner of the field.

Try This: Example 2 Continued Course The Pythagorean Theorem The segment between the two corners is the hypotenuse. The sides of the fields are legs, and they are 33 yards long and 100 yards long. 2 Make a Plan You can use the Pythagorean Theorem to write an equation. List the important information: Drawing a segment from one corner of the field to the opposite corner of the field divides the field into two right triangles.

Try This: Example 2 Continued Insert Lesson Title Here Course The Pythagorean Theorem Solve 3 a 2 + b 2 = c = c ,000 = c 2 11,089 = c  c The distance from one corner of the field to the opposite corner is about yards. Use the Pythagorean Theorem. Substitute for the known variables. Evaluate the powers. Add. Take the square roots of both sides  c Round.

Try This: Example 2 Continued Insert Lesson Title Here Course The Pythagorean Theorem Look Back 4 The hypotenuse is the longest side of a right triangle. Since the distance from one corner of the field to the opposite corner is greater than the length of either side of the field, the answer is reasonable.

Lesson Quiz: Part 1 21 in. 40 m Insert Lesson Title Here Course The Pythagorean Theorem Use the Pythagorean Theorem to find each missing length m 24 m 35 in. 28 in. 2. Find the missing length of each right triangle. 3. a =, b = 30, c = a = 20, b = 21, c =

Lesson Quiz: Part 2 5. Each rectangular section of a fence is braced by a board nailed on the diagonal of the section. The fence is 6 ft tall and the brace is 10 ft long. What is the length of the section? 8 ft Insert Lesson Title Here Course The Pythagorean Theorem