Right Triangle Worksheet

**Page 1**

1.

State which of the following measures will form a right triangle.

I. 9, 12, 15

II. 12, 16, 20

III. 12, 15, 20

I. 9, 12, 15

II. 12, 16, 20

III. 12, 15, 20

a. | I and II | ||

b. | only III | ||

c. | only II | ||

d. | only I |

In I, 15

225 = 81 + 144 = 225

The measures, 9, 12, and 15 will form a right triangle.

In II, 20

400 = 144 + 256 = 400

The measures, 12, 16, and 20 will form a right triangle.

In III, 20

400 ≠ 144 + 225 = 369, 400 is not equal to 369

The measures, 12, 15, and 20 will not form a right triangle.

So, I and II only will form right triangles.

Correct answer : (1)

2.

State which of the following measures will form a right triangle.

(i) 6, 8, 10

(ii) 3, 4, 5

(iii) 2, 3, 5

(i) 6, 8, 10

(ii) 3, 4, 5

(iii) 2, 3, 5

a. | Both (i) and (ii) | ||

b. | only (ii) | ||

c. | only (i) | ||

d. | only (iii) |

In (i), 10

100 = 36 + 64 = 100

The measures, 6, 8, and 10 will form a right triangle.

In (ii), 5

25 = 9 + 16 = 25

The measures, 3, 4, and 5 will form a right triangle.

Applying Pythagorean theorem for (iii), 5

25 ≠ 4 + 9 = 13, 25 is not equal to 13

The measures 2, 3, and 5 cannot form a right triangle.

So, (i) and (ii) only will form right triangles.

Correct answer : (1)

3.

What are the angle measures of an isosceles right triangle?

a. | 30 ^{o}, 60^{o} and 90^{o} | ||

b. | 30 ^{o}, 30^{o} and 90^{o} | ||

c. | 45 ^{o}, 45^{o}and 90^{o} | ||

d. | 40 ^{o}, 40^{o} and 100^{o} |

Sum of angles in a triangle = 180

In right triangle one angle is 90

Sum of the other two angles is 90

Since other two angles are equal, each angle = 45

[Since 90

The angle measures in a right isosceles triangle are 45

Correct answer : (3)

4.

Is every isosceles triangle an isosceles right triangle?

a. | Yes | ||

b. | No |

In right triangle, if lengths of two sides are equal then it is an isosceles right triangle.

Every isosceles triangle is not an isosceles right triangle; for example, the lengths of sides 2, 2 and 3 is an isosceles triangle.

Since 3

So, every isosceles triangle is not an isosceles right triangle.

Correct answer : (2)

5.

What type of triangle will be formed from two sides of a square field and diagonal walkway?

a. | 30 ^{o}-60^{o}-90^{o} triangle | ||

b. | 45 ^{o}-45^{o}-90^{o} triangle | ||

c. | 60 ^{o}-60^{o}-60^{o} triangle | ||

d. | None of the above |

The figure formed from the two sides of a square field and diagonal walkway is a 45

Correct answer : (2)

6.

What is the relation between the length of the shortest side and hypotenuse in a 30^{o}-60^{o}-90^{o} triangle?

a. | Shortest side is half of the hypotenuse | ||

b. | Shortest side is three times of the hypotenuse | ||

c. | Shortest side is double the hypotenuse | ||

d. | Shortest side is $\sqrt{3}$ times of the hypotenuse |

Correct answer : (1)

7.

The length of PR in the figure is 7√2 inches. What are the lengths of PQ and QR?

a. | 4 inches and 4 inches | ||

b. | 7 inches and 7 inches | ||

c. | 2 inches and 3 inches | ||

d. | 6 inches and 4 inches |

Length of PR = 7√2 inches.

In a 45

In ΔPQR, PQ and QR are congruent legs and PR is the hypotenuse.

PR = PQ√2

PQ = PR/√2

[Divide each side by √2.]

PQ = 7√2/√2

[Replace PR with 7√2.]

PQ = 7 inches

[Simplify.]

Since the lengths of two legs are equal in 45

The lengths of PQ and QR are 7 inches and 7 inches.

Correct answer : (2)

8.

Is a triangle with side lengths 4, 8 and 4√3 a 30^{o}-60^{o}-90^{o} triangle?

a. | No | ||

b. | Yes |

8

[Check for Pythagorean theorem.]

Since given measures satisfy Pythagorean theorem, they form a right triangle.

Here, the length of hypotenuse is 8 and the length of shorter leg is 4.

Since the length of hypotenuse is twice the length of shorter leg, the side lengths form a 30

Correct answer : (2)

9.

The lengths of two legs are equal and hypotenuse is $\sqrt{2}$ times the length of a leg in a triangle. Which of the following are the angles of the triangle?

a. | 60 ^{o} - 60^{o} - 60^{o} | ||

b. | 30 ^{o} - 60^{o} - 90^{o} | ||

c. | 45 ^{o} - 45^{o} - 90^{o} | ||

d. | None of the above |

The triangle is a 45

Correct answer : (3)

10.

Find the measures of the missing sides in the triangle.

a. | AB = 6 cm and AC = 6$\sqrt{2}$ cm | ||

b. | AB = 5 cm and AC = 8 cm | ||

c. | AB = 6$\sqrt{2}$ cm and AC = 6 cm | ||

d. | None of the above |

The legs have same length and hypotenuse is

AB, BC are legs and AC is the hypotenuse from the figure.

BC = AB = 6 cm

[Since legs have same lengths in an isosceles right triangle.]

AC = BC x

[Substitute BC = 6.]

The measures of the missing sides, AB = 6 cm and AC = 6

Correct answer : (1)