Free Printable Geometry Homework - Right Triangles Practice Problems

1.

Which side is the long leg in this 30-60-90 triangle?

a)

4

b)

u

c)

v

2.

Which side is the short leg of this 30-60-90 triangle?

a)

6

b)

m

c)

n

3.

Which of the following are considered special right triangles?

a)

30-60-90

b)

45-45-90

c)

20-70-90

d)

40-50-90

4.

The (a) of a right triangle create the (b) and the (c) is always the (d) side.

Choose from the below words

legs

right angle

hypotenuse

longest

shortest

acute angle

diagonal

5.

Match the following for finding sides in a 30-60-90 right triangle.

a)

Short Leg

1.

Half of the hypotenuse

b)

Hypotenuse

2.

Double the short leg

c)

Long Leg

3.

Short leg times square root of 3

6.

In a 45-45-90 right triangle, to find the measure of a leg, you take the (a) and (b) by (c) .

Choose from the below words

hypotenuse

divide

$\sqrt[]{2}$

\sqrt[]{3}

2

multiply

short leg

long leg

7.

Match the following for a 30-60-90 right triangle

a)

Short Leg

1.

Opposite the 30° angle.

b)

Long Leg

2.

Opposite the 60° angle.

c)

Hypotenuse

3.

Opposite the right angle.

8.

In a 45-45-90 right triangle, how many sides are the same size?

a)

None

b)

Two

c)

All 3

d)

Depends on the triangle

9.

If you know the value of the hypotenuse in a 45-45-90 right triangle, how would you find the measure of a leg?

a)

Divide by the square root of 2

b)

Divide by the square root of 3

c)

Multiply by 2

d)

Divide by 2

e)

None of these

10.

Label each of the following.

a)

Short Leg

b)

Long Leg

c)

Hypotenuse

1

2

3

1)

2)

3)

11.

Find the value of x.

a)

18

b)

18√3

c)

36√3

d)

12

12.

What type of special triangle is this?

a)

45°-45°-90°

b)

30°-60°-90°

c)

Equiangular

d)

Equilateral

13.

What is the length of the short side in this $30\degree-60\degree-90\degree$ triangle.

a)

x

b)

y

c)

14

14.

Find the lengths of the missing sides in this $45\degree-45\degree-90\degree$ triangle.

a)

$x=8\sqrt{2},y=16\sqrt{2}$

b)

$x=4,y=8$

c)

$x=4\sqrt{2},y=16$

d)

$x=4\sqrt{2},y=8$

15.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

16.

What is the value of x?

a)

9 in

b)

19 in

c)

81 in

d)

none of these

17.

The Pythagorean Theorem is (a) (b) (c) (d) (e)

Choose from the below words

$a^2$

$+$

$b^2$

$=$

$c^2$

$x^2$

$-$

$\times$

$\div$

18.

What is the final step in solving this work for c?
a² + b² = c²
3² + 4² = c²
9 + 16 = c²
25 = c²

a)

Divide both sides by 2

b)

Take the square root of both sides

c)

25 IS the final answer

19.

Do the sides make a right triangle?

sides 9 ft, 20 ft, 14 ft

a)

no

b)

yes

20.

Jane and Miguel are siblings. They go to different schools. Jane walks 6 blocks east from home. Miguel walks 8 blocks north. How many blocks apart would the two schools be if you could walk straight from one school to the other?

a)

14

b)

10

c)

5.3

d)

2

21.

The diagonal of a rectangle is 25 inches. The width is 15 inches. What is the area of the rectangle?

a)

375 in²

b)

70 in²

c)

300 in²

d)

20 in²

Geometry Homework - Right Triangles Practice Problems

Total questions: 21

Worksheet time: 47mins

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