Free Printable Understanding Right Triangles and Theorems

Worksheets

Understanding Right Triangles and Theorems

Total questions: 38

Worksheet time: 2hrs 59mins

Name

Class

Date

What is a right triangle?

A triangle where all sides equal 90 degrees

A triangle where every angle is 90 degrees

A triangle where all three sides are equal

A triangle where there is a 90 degree angle

What letter represents the hypotenuse?

a and b

Hypotenuse

Vertical side in a right triangle

Longest side in a right triangle

Horizontal side in a right triangle

a²+ b²= c²

Which choice represents the legs?

a and b

Define the term 'right angle'

Three angles in a right triangle

When two angles in a triangle are 90 degrees

Any angle less than 90 degrees

A 90 degree angle

The Pythagorean Theorem is _________

a + b = c

a² + b² = c²

a² + b² + c²

A = LW

Which equation can be used to solve for "x"?

15² – x² = 21²

x² – 15² = 21²

15² + 21² = x²

21² – 15² = x²

Determine the length of the missing side.

Do the segment lengths 15, 12, and 9 form a right triangle?

Yes

Maybe

Pythagoras

10.

Does the set of numbers represent a right triangle?

20, 25, 15

Yes

11.

The Pythagorean Theorem ONLY works on which triangle?

Obtuse

Right

Acute

Isosceles

12.

What is the side of a right triangle across from the right angle called?

Square

Arm

Leg

Hypotenuse

13.

If a right triangle has side lengths 6, 6.7 and 3, which side is the hypotenuse?

6.7

Not enough information

14.

Find the length of the missing side

15.

Side c on a right triangle is ALWAYS the longest.

True

False

16.

Find the length of the missing side

17.

Is this a right triangle

Yes

18.

In a right triangle, if a = 8 and c = 17, what is the correct setup to find the value of b?

$17^2+8^2=b^2$

$8^2+b^2=17^2$

$17^2+b^2=8^2$

$\frac{8^2}{b^2}=\frac{17^2}{100}$

19.

What is the opposite of squaring a number

divide

multiply

square root

fractions

20.

The Pythagorean is used to find what

missing sides only

missing angles only

either missing sides or angles

21.

John leaves school to go home. He walks 6 blocks North and then 8 blocks west. How far is John from the school?

14 blocks

12 blocks

10 blocks

8.5 blocks

22.

What is the formula for Pythagorean Theorem?

a^2+b^2=c^2

b-a=c

c^2+b^2=a^2

a+b=c

23.

Which set of sides would make a right triangle?

4,5,6

8,10,12

5,12,13

5,10,12

24.

^{Find the length of the missing side}

108

83.6

25.

What is the diagonal length of the iPad?

9.2 in

11 in

13 in

9.6 in

26.

_{^{Find the missing side}}

6.4

6.2

27.

Tanya runs diagonally across a rectangular field that has a length of 40 yards and a width of 30 yards. What is the length of the diagonal, in yards, that Tanya runs?

26.5 yards

10 yards

50 yards

46.7 yards

28.

Which equation is modeled by the picture shown?

3²+5²=4²

3²+4²=5²

5²+4²=3²

9²+16²=25²

29.

The slide at the playground has a height of 6 feet. The base of the slide measured on the ground is 8 feet. What is the length of the slide?

8 feet

5.29 feet

10 feet

14 feet

30.

The bottom of a 13-foot straight ladder is set into the ground 5 feet away from a wall. When the top of the ladder is leaned against the wall, what is the distance above the ground it will reach?

12 feet

13.9 feet

31.

A baseball "diamond" is actually a square with sides of 90 feet. If a runner tries to steal second base, how far must the catcher, at home plate, throw to get the runner "out"? (Distance across the diagonal)

180 feet

90 feet

13.4 feet

127.3 feet

32.

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

17 miles

32 miles

37 miles

40 miles

33.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

25 feet

26 feet

27 feet

28 feet

34.

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?

5.3

35.

A piece of paper that Brittany has is 11 inches tall and 8 inches wide. She draws a straight line diagonally across the paper. How long is the line she drew?

7.5 in

12.4 in

13.6 in

14.3 in

36.