Converse of the Pythagorean Theorem Worksheet

**Page 2**

11.

Find the value of $x$ in the right triangle.

a. | 12 | ||

b. | 16 | ||

c. | 13 | ||

d. | 3 |

[Write Pythagorean theorem.]

[Substitute for

[Simplify.]

72 = 6

[Subtract (

[Divide each side by 6.]

= 12

Correct answer : (1)

12.

Find the value of $x$ in the figure.

a. | 30.25 | ||

b. | 36.24 | ||

c. | 28.125 | ||

d. | 35.8 |

15

[Use Pythagorean theorem.]

225 +

[Apply exponents.]

225 = 8

[Add 4

[Divide each side by 8.]

= 28.125

The value of

Correct answer : (3)

13.

A ladder which is 15 feet long is placed on a wall such that the top of the ladder touches the top of the wall. The bottom of the ladder is 9 feet away from the wall. What is the height of the wall?

a. | 15 feet | ||

b. | 18 feet | ||

c. | 12 feet | ||

d. | 9 feet |

The distance from the foot of the ladder to the wall,

Let

[Write Pythagorean theorem.]

[Subtract

= 15

[Substitute

= 225 - 81

[Apply exponents and simplify.]

= 144

[Take square root of both sides.]

= 12

Height of the wall = 12 feet.

Correct answer : (3)

14.

State whether the lengths 9, 10 and 11 are sides of a right triangle.

a. | data insufficient | ||

b. | yes | ||

c. | cannot say | ||

d. | no |

[Check for Pythagorean theorem.]

The lengths 9, 10 and 11 do not satisfy the Pythagorean theorem.

The lengths 9, 10 and 11 are not sides of a right triangle.

Correct answer : (4)

15.

Find the measures of the sides of the right triangle shown.

a. | 3, 4 and 6 | ||

b. | 5, 12 and 13 | ||

c. | 4, 11 and 13 | ||

d. | 6, 8 and 10 |

[Write Pythagorean theorem.]

(2

[Substitute for

4

4

[Subtract (9

[Divide each side by 4

2

[Substitute

3

[Substitute

3

[Substitute

The measures of the sides of the given right triangle are 6, 8 and 10.

Correct answer : (4)

16.

Find the length of AC in the dot paper, if the distance between each dot is one unit.

a. | 10$\sqrt{5}$ units | ||

b. | 8$\sqrt{5}$ units | ||

c. | 5$\sqrt{5}$ units | ||

d. | 8 units |

AC

[Apply Pythagorean theorem.]

AC

[Substitute the values of AB and BC.]

AC

[Apply exponents and simplify.]

AC =

[Take square root of both sides.]

The length of AC is 5

Correct answer : (3)

17.

What are the side measures of the blue colored right triangle enclosed in the dot paper, if the distance between each dot is one unit?

a. | 3, 2 and 5 | ||

b. | 5, 6 and 9 | ||

c. | 10, 11 and 18 | ||

d. | 3, 2 and $\sqrt{13}$ |

(Hypotenuse)

[Apply Pythagorean theorem.]

= 9 + 4

[Apply exponents.]

= 13

Hypotenuse =

[Take square root of both sides.]

The side measures of the right triangle are 3 units, 2 units and

Correct answer : (4)

18.

What are the measures of the sides of right triangle AED in the figure, if the distance between two dots in the figure is one unit?

a. | 3, 8 and 25 | ||

b. | 2, 3 and 5 | ||

c. | 2, 3 and $\sqrt{13}$ | ||

d. | 4, 9 and 13 |

AD

[Apply Pythagorean theorem.]

= 2

[Substitute the values of AE and DE.]

= 4 + 9

[Apply exponents and simplify.]

= 13

AD =

[Take square root on both sides.]

The side measures of the right triangle are 2 units, 3 units and

Correct answer : (3)

19.

What is the length of the third side of the triangle shown in the figure?

a. | 4 | ||

b. | $\sqrt{15}$ | ||

c. | $\sqrt{34}$ | ||

d. | $\sqrt{8}$ |

The side opposite to the right angle is hypotenuse.

Let

Applying Pythagorean theorem,

[Apply exponents and add.]

[Take square root on both the sides.]

The third side of the triangle is

Correct answer : (3)

20.

What are the values of $x$ and $y$ in the triangle?

a. | 4 units and 15 units | ||

b. | 2$\sqrt{5}$ units and 45 units | ||

c. | $\sqrt{160}$units and $\sqrt{41}$ units | ||

d. | 24 units and 45 units |

BC

[Apply Pythagorean theorem.]

[Substitute BC, BD and CD.]

[Evaluate powers and simplify.]

[Take square root both sides.]

ΔADC is a right triangle.

AC

[Apply Pythagorean theorem.]

[Substitute AC, AD and CD.]

[Evaluate powers and simplify.]

[Take square root both sides.]

Correct answer : (3)