WARM UP What is the Pythagorean Theorem? You place a 10-foot ladder against a wall. If the base of the ladder is 3 feet from the wall, how high up the wall does the ladder reach? A 48-inch wide screen television means that the measure along the diagonal is 48 inches. If the screen is a square, what are the dimensions of the length and width?

9.2 THE PYTHAGOREAN THEOREM

LEARNING OUTCOMES I will be able to use the Pythagorean Theorem to find missing pieces in a right triangle. I will be able to use the Pythagorean Theorem to help classify a triangle.

PIECES OF A RIGHT TRIANGLE What are the different pieces of a right triangle? a c b = hypotenuse = leg

THE PYTHAGOREAN THEOREM The Pythagorean Theorem is a² + b² = c². This allows us to solve for the hypotenuse of a right triangle given the legs. We can use this equation to solve for a leg, given the hypotenuse and another leg. c² - b² = a² where a is the unknown leg.

SAGE AND SCRIBE Give the exact answer for the missing side lengths. Make sure to simplify all radicals

PROVING THE PYTHAGOREAN THEOREM With your partner see if you can come up with a proof for the Pythagorean Theorem. Hint: Use similar Triangles.

PYTHAGOREAN TRIPLES Pythagorean Triples are three integers that create a right triangle. The most popular Pythagorean Triple is a Triangle. Name another Pythagorean Triple similar to a Triangle? Another popular Pythagorean Triple is a triangle.

9.3 THE CONVERSE OF THE PYTHAGOREAN THEOREM

THE PYTHAGOREAN THEOREM Does the Pythagorean Theorem work for any triangle?

JIGSAW ACTIVITY 1’s – Draw an acute triangle 2’s – Draw an obtuse triangle 3’s – Draw a right triangle After drawing your triangle measure the side lengths as to the nearest centimeter Plug your side lengths into the Pythagorean Theorem, where c is the longest side.

JIGSAW ACTIVITY What do you notice about your a² + b² sides and your c² sides. Discuss with others that have the same number as you. Form a group of three so there is a 1, 2 and 3 in your group. Discuss the differences in your triangles. In your group come up with rules for when you know you have an acute, obtuse or right triangle based on the side lengths.

JIGSAW ACTIVITY Conclusions: If a² + b² = c², then the triangle is right. If a² + b² > c², then the triangle is acute. If a² + b² < c², then the triangle is obtuse.

CLASSIFYING TRIANGLES

CLASSIFYING TRIANGLES (YOUR TURN) Determine whether you can create a triangle with the side lengths. If you can, use the Pythagorean Theorem to classify the triangle as right, acute or obtuse. 1.) 20, 99, 1012.) 2, 10, 13 Yes; Right TriangleNo 3.) 26, 10, 174.) 10, 11, 14 Yes; Obtuse TriangleYes; Acute Triangle

EXIT TICKETHOMEWORK Do these side lengths form a Right Triangle, Acute Triangle or Obtuse Triangle. Show Work! 10, 49, 50 Pg. 819: 7-15, 19-27