Find X. 9. SOLUTION: in a Right Triangle, the Sum of the Squares Of

Find x.

9. SOLUTION: 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. The length of the hypotenuse is x and the lengths of the legs are 12 and 16.

10. SOLUTION: 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. The length of the hypotenuse is 15 and the lengths of the legs are 9 and x.

8-2 The Pythagorean Theorem and Its Converse

Find x.

11. SOLUTION: 9. In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length SOLUTION: of the hypotenuse. The length of the hypotenuse is 5 In a right triangle, the sum of the squares of the and the lengths of the legs are 2 and x. lengths of the legs is equal to the square of the length of the hypotenuse. The length of the hypotenuse is x and the lengths of the legs are 12 and 16.

12. SOLUTION: In a right triangle, the sum of the squares of the 10. lengths of the legs is equal to the square of the length SOLUTION: of the hypotenuse. The length of the hypotenuse is 66 and the lengths of the legs are 33 and x. 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. The length of the hypotenuse is 15 and the lengths of the legs are 9 and x.

13. eSolutions11. Manual - Powered by Cognero SOLUTION: Page 1 SOLUTION: In a right triangle, the sum of the squares of the In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length lengths of the legs is equal to the square of the length of the hypotenuse. The length of the hypotenuse is x

of the hypotenuse. The length of the hypotenuse is 5 and the lengths of the legs are . and the lengths of the legs are 2 and x.

12. SOLUTION: 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. The length of the hypotenuse is 66 and the lengths of the legs are 33 and x. 14.

SOLUTION: 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. The length of the hypotenuse is

and the lengths of the legs are .

13. SOLUTION: 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. The length of the hypotenuse is x

and the lengths of the legs are . Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer. 21. 7, 15, 21 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Therefore, the set of numbers can be measures of a triangle.

Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides.

14. SOLUTION:

In a right triangle, the sum of the squares of the Therefore, by Pythagorean Inequality Theorem, a lengths of the legs is equal to the square of the length triangle with the given measures will be an obtuse of the hypotenuse. The length of the hypotenuse is triangle.

and the lengths of the legs are . 22. 10, 12, 23 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Since the sum of the lengths of two sides is less than that of the third side, the set of numbers cannot be measures of a triangle.

23. 4.5, 20, 20.5 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the Determine whether each set of numbers can be length of the third side. the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer. 21. 7, 15, 21 Therefore, the set of numbers can be measures of a SOLUTION: triangle.

By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the Classify the triangle by comparing the square of the length of the third side. longest side to the sum of the squares of the other

two sides.

Therefore, the set of numbers can be measures of a triangle.

Now, classify the triangle by comparing the square of Therefore, by the converse of Pythagorean Theorem, the longest side to the sum of the squares of the a triangle with the given measures will be a right other two sides. triangle.

24. 44, 46, 91 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Therefore, by Pythagorean Inequality Theorem, a

triangle with the given measures will be an obtuse triangle.

22. 10, 12, 23 Since the sum of the lengths of two sides is less than SOLUTION: that of the third side, the set of numbers cannot be By the triangle inequality theorem, the sum of the measures of a triangle. lengths of any two sides should be greater than the length of the third side. 25. 4.2, 6.4, 7.6 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Since the sum of the lengths of two sides is less than that of the third side, the set of numbers cannot be measures of a triangle.

23. 4.5, 20, 20.5 Therefore, the set of numbers can be measures of a triangle. SOLUTION: By the triangle inequality theorem, the sum of the Now, classify the triangle by comparing the square of lengths of any two sides should be greater than the the longest side to the sum of the squares of the length of the third side. other two sides.

Therefore, the set of numbers can be measures of a triangle. Therefore, by Pythagorean Inequality Theorem, a Classify the triangle by comparing the square of the triangle with the given measures will be an acute longest side to the sum of the squares of the other triangle. two sides. 26. 4 , 12, 14 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Therefore, by the converse of Pythagorean Theorem, a triangle with the given measures will be a right triangle.

24. 44, 46, 91 Therefore, the set of numbers can be measures of a triangle. SOLUTION: By the triangle inequality theorem, the sum of the Now, classify the triangle by comparing the square of lengths of any two sides should be greater than the the longest side to the sum of the squares of the length of the third side. other two sides.

Since the sum of the lengths of two sides is less than that of the third side, the set of numbers cannot be Therefore, by Pythagorean Inequality Theorem, a measures of a triangle. triangle with the given measures will be an obtuse triangle. 25. 4.2, 6.4, 7.6 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Therefore, the set of numbers can be measures of a triangle.

Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides.

Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an acute triangle.

26. 4 , 12, 14 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Therefore, the set of numbers can be measures of a triangle.

Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides.

Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an obtuse triangle. Find x.

Find x. 10. SOLUTION: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length 9. of the hypotenuse. The length of the hypotenuse is 15 and the lengths of the legs are 9 and x. SOLUTION: 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. The length of the hypotenuse is x and the lengths of the legs are 12 and 16.

11. SOLUTION: 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. The length of the hypotenuse is 5 10. and the lengths of the legs are 2 and x. SOLUTION: 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. The length of the hypotenuse is 15 and the lengths of the legs are 9 and x.

12. SOLUTION: 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. The length of the hypotenuse is 66 11. and the lengths of the legs are 33 and x. SOLUTION: 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. The length of the hypotenuse is 5 and the lengths of the legs are 2 and x.

13. SOLUTION: In a right triangle, the sum of the squares of the 12. lengths of the legs is equal to the square of the length SOLUTION: of the hypotenuse. The length of the hypotenuse is x

In a right triangle, the sum of the squares of the and the lengths of the legs are . lengths of the legs is equal to the square of the length of the hypotenuse. The length of the hypotenuse is 66 and the lengths of the legs are 33 and x.

8-2 The Pythagorean Theorem and Its Converse

13.

SOLUTION: 14. In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length SOLUTION: of the hypotenuse. The length of the hypotenuse is x In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length and the lengths of the legs are . of the hypotenuse. The length of the hypotenuse is

and the lengths of the legs are .

Determine whether each set of numbers can be the measures of the sides of a triangle. If so, 14. classify the triangle as acute, obtuse, or right. SOLUTION: Justify your answer. In a right triangle, the sum of the squares of the 21. 7, 15, 21 lengths of the legs is equal to the square of the length SOLUTION: of the hypotenuse. The length of the hypotenuse is By the triangle inequality theorem, the sum of the and the lengths of the legs are . lengths of any two sides should be greater than the length of the third side.

Therefore, the set of numbers can be measures of a triangle.

Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides. eSolutions Manual - Powered by Cognero Page 2

Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an obtuse triangle. Determine whether each set of numbers can be the measures of the sides of a triangle. If so, 22. 10, 12, 23 classify the triangle as acute, obtuse, or right. Justify your answer. SOLUTION: 21. 7, 15, 21 By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the SOLUTION: length of the third side. By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Since the sum of the lengths of two sides is less than that of the third side, the set of numbers cannot be Therefore, the set of numbers can be measures of a measures of a triangle. triangle. 23. 4.5, 20, 20.5 Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the SOLUTION: other two sides. By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Therefore, by Pythagorean Inequality Theorem, a Therefore, the set of numbers can be measures of a

triangle with the given measures will be an obtuse triangle. triangle. Classify the triangle by comparing the square of the longest side to the sum of the squares of the other 22. 10, 12, 23 two sides. SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Therefore, by the converse of Pythagorean Theorem, a triangle with the given measures will be a right triangle. Since the sum of the lengths of two sides is less than 24. 44, 46, 91 that of the third side, the set of numbers cannot be measures of a triangle. SOLUTION: By the triangle inequality theorem, the sum of the 23. 4.5, 20, 20.5 lengths of any two sides should be greater than the SOLUTION: length of the third side. By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Since the sum of the lengths of two sides is less than that of the third side, the set of numbers cannot be Therefore, the set of numbers can be measures of a measures of a triangle. triangle. 25. 4.2, 6.4, 7.6 Classify the triangle by comparing the square of the SOLUTION: longest side to the sum of the squares of the other By the triangle inequality theorem, the sum of the two sides. lengths of any two sides should be greater than the length of the third side.

Therefore, the set of numbers can be measures of a Therefore, by the converse of Pythagorean Theorem, triangle. a triangle with the given measures will be a right triangle. Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the 24. 44, 46, 91 other two sides. SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an acute triangle. Since the sum of the lengths of two sides is less than 26. 4 , 12, 14 that of the third side, the set of numbers cannot be measures of a triangle. SOLUTION: By the triangle inequality theorem, the sum of the 25. 4.2, 6.4, 7.6 lengths of any two sides should be greater than the SOLUTION: length of the third side. By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Therefore, the set of numbers can be measures of a triangle.

Therefore, the set of numbers can be measures of a Now, classify the triangle by comparing the square of triangle. the longest side to the sum of the squares of the other two sides. Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides.

Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an obtuse triangle. Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an acute triangle.

26. 4 , 12, 14 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Therefore, the set of numbers can be measures of a triangle.

Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides.

Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an obtuse triangle. Find x.

Find x.

9. SOLUTION: 11. In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length SOLUTION: of the hypotenuse. The length of the hypotenuse is x In a right triangle, the sum of the squares of the and the lengths of the legs are 12 and 16. lengths of the legs is equal to the square of the length of the hypotenuse. The length of the hypotenuse is 5 and the lengths of the legs are 2 and x.

10. SOLUTION: 12. In a right triangle, the sum of the squares of the SOLUTION: lengths of the legs is equal to the square of the length In a right triangle, the sum of the squares of the of the hypotenuse. The length of the hypotenuse is 15 lengths of the legs is equal to the square of the length and the lengths of the legs are 9 and x. of the hypotenuse. The length of the hypotenuse is 66 and the lengths of the legs are 33 and x.

11. SOLUTION: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length 13. of the hypotenuse. The length of the hypotenuse is 5 SOLUTION: and the lengths of the legs are 2 and x. 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. The length of the hypotenuse is x

and the lengths of the legs are .

14. SOLUTION: 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. The length of the hypotenuse is

and the lengths of the legs are .

13. SOLUTION: 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. The length of the hypotenuse is x

and the lengths of the legs are .

Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer. 21. 7, 15, 21 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Therefore, the set of numbers can be measures of a triangle.

Now, classify the triangle by comparing the square of 14. the longest side to the sum of the squares of the SOLUTION: other two sides. 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. The length of the hypotenuse is

and the lengths of the legs are .

Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an obtuse triangle.

22. 10, 12, 23 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Since the sum of the lengths of two sides is less than 8-2 The Pythagorean Theorem and Its Converse that of the third side, the set of numbers cannot be measures of a triangle.

Determine whether each set of numbers can be 23. 4.5, 20, 20.5 the measures of the sides of a triangle. If so, SOLUTION: classify the triangle as acute, obtuse, or right. Justify your answer. By the triangle inequality theorem, the sum of the 21. 7, 15, 21 lengths of any two sides should be greater than the length of the third side. SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Therefore, the set of numbers can be measures of a triangle.

Classify the triangle by comparing the square of the Therefore, the set of numbers can be measures of a longest side to the sum of the squares of the other triangle. two sides.

Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides.

Therefore, by the converse of Pythagorean Theorem, a triangle with the given measures will be a right triangle.

Therefore, by Pythagorean Inequality Theorem, a 24. 44, 46, 91 triangle with the given measures will be an obtuse SOLUTION: triangle. By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the 22. 10, 12, 23 length of the third side.

SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Since the sum of the lengths of two sides is less than that of the third side, the set of numbers cannot be measures of a triangle.

25. 4.2, 6.4, 7.6 Since the sum of the lengths of two sides is less than that of the third side, the set of numbers cannot be SOLUTION: measures of a triangle. By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the 23. 4.5, 20, 20.5 length of the third side.

SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Therefore, the set of numbers can be measures of a triangle.

Now, classify the triangle by comparing the square of eSolutions Manual - Powered by Cognero the longest side to the sum of the squares of the Page 3 Therefore, the set of numbers can be measures of a other two sides.

triangle.

Classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides.

Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an acute triangle.

26. 4 , 12, 14 Therefore, by the converse of Pythagorean Theorem, a triangle with the given measures will be a right SOLUTION: triangle. By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the 24. 44, 46, 91 length of the third side.

SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Therefore, the set of numbers can be measures of a triangle.

Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides. Since the sum of the lengths of two sides is less than that of the third side, the set of numbers cannot be measures of a triangle.

25. 4.2, 6.4, 7.6 SOLUTION: By the triangle inequality theorem, the sum of the Therefore, by Pythagorean Inequality Theorem, a lengths of any two sides should be greater than the triangle with the given measures will be an obtuse

length of the third side. triangle.

Therefore, the set of numbers can be measures of a triangle.

Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides.

Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an acute triangle.

26. 4 , 12, 14 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Therefore, the set of numbers can be measures of a triangle.

Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides.

Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an obtuse triangle. Find x.

11. SOLUTION: 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. The length of the hypotenuse is 5 and the lengths of the legs are 2 and x.

13. SOLUTION: 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. The length of the hypotenuse is x

and the lengths of the legs are .

14. SOLUTION: 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. The length of the hypotenuse is

and the lengths of the legs are .

Therefore, the set of numbers can be measures of a triangle.

Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides.

Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an obtuse triangle.

22. 10, 12, 23 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Since the sum of the lengths of two sides is less than that of the third side, the set of numbers cannot be measures of a triangle.

23. 4.5, 20, 20.5 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Therefore, the set of numbers can be measures of a triangle.

Classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides.

Therefore, by the converse of Pythagorean Theorem, a triangle with the given measures will be a right triangle.

24. 44, 46, 91 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Since the sum of the lengths of two sides is less than 8-2 Thethat ofPythagorean the third side, Theorem the set of and numbers Its Converse cannot be measures of a triangle.

25. 4.2, 6.4, 7.6 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Therefore, the set of numbers can be measures of a triangle.

Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides.

Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an acute triangle.

26. 4 , 12, 14 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Therefore, the set of numbers can be measures of a triangle.

Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides.

Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an obtuse triangle.