P.O. Use the Pythagorean Theorem to solve problems.

L.O. I can use the Pythagorean Property to find unknown lengths in right triangles.

E.Q. What is the Pythagorean Property? How do we use it in order to find unknown lengths in right triangles?

History Link

Pythagorus of Samoa was the ancient Greek mathematician after whom the property is named. He thought that everything in the universe could be explained by using counting numbers.

Vocabulary:

Leg Each of the two shorter sides of a right triangle is a leg.

Hypotenuse The longest, side opposite the right angle.

Bell Work

Draw this triangle and name the parts!

Think and Discuss

Do all triangles contain a hypotenuse? Why or Why not

Vocabulary:

Pythagorean Property

In any right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

Example #1 A right triangle has legs measuring 7 in.

and 24 in. What is the length of the hypotenuse?

Example #2

The hypotenuse of a right triangle is 17 cm. long, and one leg is 8 cm. long. How long is the other leg?

Think and DiscussTurn to your shoulder partner and discuss the

following question.

Must the hypotenuse be the longest side of a right triangle? Explain.

Yes, the hypotenuse is the side opposite the angle with the greatest measure 90 degrees.

Example #3

A right triangle has a hypotenuse of length 29 ft and one leg of length 20 ft. Find the length of the hypotenuse.

Guided PracticeWork with your shoulder partner to discus how the problem would solved. Solve together.1. 2. a = 9 cm; b= 12 cm.

Find C

1. Find the hypotenuse if the legs measure 6 m and 8 m.

2. Find the hypotenuse if the legs measure 5 m and 12 m.3. Find the missing leg if the hypotenuse measures 9 ft and one leg measures 7 ft.4. Find the missing leg if the hypotenuse measures 7 cm and one leg measures 4 cm.

5. How do you find the length of the hypotenuse of a right triangle if you know the lengths of both legs?

Think and DiscussTurn to your shoulder partner and discuss the

following question.

The sides of a triangle are 9 ft., 12 ft., and 16 ft. How can you tell if the triangle is a right triangle?

Ticket out

1. How do you find the length of the hypotenuse of a right triangle if you know the lengths of both legs?

2. How do you find the length of a leg of a right triangle if you know the length of the other leg and the length of the hypotenuse?

Are these the correct measurements?

P.O. Use the Pythagorean Theorem to solve problems.

L.O. I can compute unknown lengths such as distances between cities on a map.

E.Q. What is the Pythagorean Property? How do we use it in order to find unknown lengths in real life problems?

Motivate

Evelyn walks 6 miles due north and Harley walks 8 miles due east from the same point. How far apart are they?

Challenge:

Describe ways to apply the pythagorean Theorem in real life. Think about measuring distances, about carpentry, and about architecture.

Example 1

The direct air distance from Chicago to Denver is 920 mi. It is 580 mi from Chicago to Birmingham. How far is it from Denver to Birmingham?

Example 2

Merritt is buying a board to use as a diagonal brace on a rectangular gate. The gate is 36 in. wide and 42 in. high. What should be the length of the board?

Guided Practice

A train leaves a station and travels 60 mi north. A second train leaves the station and travels 30 mi west. How far apart are they?

Draw the diagram and label the right angles according to the

information in the problem before writing and solving the equation.

Guided Practice To decorate for a party, Mrs. Burr strung a 20 ft banner across the diagonal of her living room. The living room is 17 ft long. How wide is it?

Draw the diagram and label the right angles according to the

information in the problem before writing and solving the equation.

Pg. 550 1-4; 1-8: Working with a shoulder partner, decide who is going to complete the even numbers and who would complete the odd numbers. Solve the problems. Trade papers when you are finished and score for correct responses.1. Person does not understand at all.2. Person kinda gets it.3. Perfection.

You need to explain the reason for your score.

Independent Practice

Word problemIf you drove 165 mi south from Cleveland and then 145 mi west, you would be in Cincinnati. Suppose a new highway is built, connecting them in a straight line. Find how long the highway would be, to the nearest tenth mile. Draw a picture, and then solve.