1. Use the Pythagorean Theorem to see if the measurements below can form a right triangle. ***** a = 5 in. b = 12 in. c = 13 in.

Yes, it is a right triangle.

No, it is not a right triangle

There is not enough info.

2. a = 6.4, b = 12, c = 12.2 is this a right triangle?

yes

no

3. a = 2.1, b = 7.2, c = 7.5 is this a right triangle?

yes

no

4. If a triangle has a side a=5 and b=12, what is c?

10

17

169

13

5. Which three side lengths form a right triangle?

5, 12, 13

4, 5, 7

3, 6, 9

1, 3, square root of 11

6. Use the Pythagorean Theorem to see if the measurements below can form a right triangle. **** a= 6 cm, b= 8 cm, c = 10 cm

Yes, it is a right triangle.

No, it is not a right triangle

There is not enough info.

7. What is the length of x?

5

7

8

25

8. Solve for c

33

11.2

11.4

13

9. Solve for x

10

11.4

13

2

10. Find the hypotenuse in the image shown

169

13

14.4

17

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

Yes

No

Maybe

Pythagoras

12. Do the segment lengths 9, 11 and 15 cm form a right triangle?

yes

no

maybe

pythagoras

13. Given the 3 lengths of a triangle are 6 in, 8 in and 10 in. Will this make a right triangle?

yes

no

maybe

22

14. The Pythagorean Theorem ONLY works on which triangle?

obtuse

scalene

isosceles

right

15. What is the name of the longest side of a right-angled triangle?

Pythagoras

Hypotenoose

Hipotenuse

Hypotenuse

16. What kind of triangles does the Pythagorean Theorem work with?

Right

Left

Isosceles

Equilateral

17. What is the formula for Pythagoras theorem if in a right angles triangle a and b are the short sides and c is the longest side?

a2 x b2 = c2

a + b = c

a2 + a2 = c2

a2 + b2 = c2

18. Does an 8, 15, 16 triangle have a Right Angle?

yes

no

19. To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk 34 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond?

35

22

58

75

20. John runs diagonally across a rectangular field that has a length of 40 yards and a width of 30 yards, as shown in the diagram.What is the length of the diagonal, in yards, that John runs?

50

60

70

80

21. Does this triangle have a Right Angle?

No

Yes

Terms and Answers to Learn

Pythagorean Theorem Formula

Pythagorean Theorem Definition

A right triangle (with a 90 degree angle) is composed of two legs and a hypotenuse (side opposite the right angle).

Pythagorean Theorem

Pythagorean Theorem

Example: Pythagorean Theorem

Legs

Sides that are adjacent (same vertex, share a common side) the right angle. There are two.

Hypotenuse

The side opposite the right angle

Right Triangle

A triangle that has one right angle (90 degrees) with 2 legs, and one hypotenuse.

leg

Either of the two shortest sides of a right triangle, they meet at a common vertex to form a right angle.

hypotenuse

The longest side of a right triangle. It is always opposite of, and never is a part of, the right angle.

square

The result of multiplying a number by itself.

root (of a square)

Any side of a square. A number which, when multiplied by itself, makes a square. One of the dimensions of a square.

pythagorean theorem

The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

perfect square

A square with a whole number root.

Pythagoras

Greek philosopher, 570-495 BC. There is no evidence that Pythagoras himself worked on or proved the Pythagorean Theorem, which was used previously by Babylonians and Indians.

right triangle

A triangle that contains a right angle.

right angle

An angle of exactly 90 degrees.

inverse operations

Math operations that reverse the effect of each other.

c, and the longest side of a right triangle

Hypotenuse

labeled a and b, the other two sides of the right triangle

Leg

the square of the hypotenuse is equal to
the sum of the squares of the other two sides.

Pythagorean Theorem

5

a=3 b=4 c=?

25

a=7 b=24 c=?

10

a=6 b=8 c=?

No

Is this a right triangle: a=4, b=6, c=9

yes

Is this a right triangle: a=5 b=12 c=13

a triangle where one angle is guaranteed to be 90 degrees.

Right Triangle

yes

Would these three sides form a right angle 8, 15, 17

12

Which side length would be considered c? 9,12,10

12

Find b: a=5 b=? c=13

Either of the two shortest sides of a right triangle, they meet at a common vertex to form a right angle.

leg

The longest side of a right triangle. It is always opposite of, and never is a part of, the right angle.

hypotenuse

The result of multiplying a number by itself.

square

The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

pythagorean theorem

A square with a whole number root.

perfect square

Greek philosopher, 570-495 BC. There is no evidence that Pythagoras himself worked on or proved the Pythagorean Theorem, which was used previously by Babylonians and Indians.

Pythagoras

A triangle that contains a right angle.

right triangle

An angle of exactly 90 degrees.

right angle

Math operations that reverse the effect of each other.

inverse operations

A right triangle (with a 90 degree angle) is composed of two legs and a hypotenuse (side opposite the right angle).

Pythagorean Theorem Definition

Sides that are adjacent (same vertex, share a common side) the right angle. There are two.

Legs

The side opposite the right angle

Hypotenuse

A triangle that has one right angle (90 degrees) with 2 legs, and one hypotenuse.

Right Triangle

Right triangle geometric means formula

a=square root of b*c
d=square root of b+c * b
e=square root of b+c * c

How to recognize a right triangle

c2=a2+b2

How to recognize an obtuse triangle

c2>a2+b2

How to recognize an acute triangle

c2<a2+b2

How to solve 30-60-90 triangles

hypotenuse is 2b, legs are b and b square root of 3

How to solve 45-45-90 triangles

hypotenuse is a square root of 2, legs are same length

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