Assignment P : 1, 2-26 even, 29, 32, 33, 35, 36, 38, 46, 47 Challenge Problems

Example 1 Find the length of the hypotenuse of the right triangle.

Example 2 1.What is the Converse of the Pythagorean Theorem? 2.If x, y, and z are the lengths of the 3 sides of a triangle and they work in the Pythagorean formula, then is the triangle a right triangle?

Investigation 1 In this investigation you will use string to construct triangles whose sides have lengths that are Pythagorean triples. Then we will see if the triangle you made is indeed a right triangle.

Investigation 1 Step 1: Select a set of Pythagorean triples from the previous list. Mark off points A, B, C, and D on a string to create lengths from your set of Pythagorean triples. For example, mark off segments 8 cm, 15 cm, and 17 cm long.

Investigation 1 Step 2: Hold the two ends together (points A and D) while a group member holds point B and another holds point C. Carefully stretch the rope tight to form a triangle.

Investigation 1 Step 3: With a protractor, measure the largest angle or use a corner of a piece of paper to test for a right angle.

Investigation 1 Was your figure close to a right triangle? Try this investigation again by selecting another set of lengths from the list of Pythagorean triples. Do you get a right triangle?

7.2 Converse of the Pythagorean Theorem Objectives: 1.To investigate and use the Converse of the Pythagorean Theorem 2.To classify triangles when the Pythagorean formula is not satisfied

Theorem! Converse of the Pythagorean Theorem If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then it is a right triangle.

Example 3 Which of the following is a right triangle?

Example 4 Tell whether a triangle with the given side lengths is a right triangle. 1.5, 6, 7 2.5, 6, 3.5, 6, 8

Investigation 2 In the previous example, the side lengths 5 and 6 do not make a right triangle when paired with either 7 or 8. So what kind of triangle do these side lengths make?

Theorems! Acute Triangle Theorem If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then it is an acute triangle.

Theorems! Obtuse Triangle Theorem If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then it is an obtuse triangle.

Example 5 Can segments with lengths 4.3 feet, 5.2 feet, and 6.1 feet form a triangle? If so, would the triangle be acute, right, or obtuse?

Example 6 The first steel squares were manufactured by the Eagle Steel Company in the 1820s. These are now used by carpenters everywhere to check and construct right angles.

Example 6 Prior to the invention of this tool, carpenters used a good old- fashioned tape measure and the Converse of the Pythagorean Theorem. How do you think this was accomplished?

Example 7 The sides of an obtuse triangle have lengths x, x + 3, and 15. What are the possible values of x if 15 is the longest side of the triangle?

Assignment P : 1, 2-26 even, 29, 32, 33, 35, 36, 38, 46, 47 Challenge Problems