Pythagorean Theorem & Special Right Triangles

Pythagorean Theorem and Special Right Triangles

Dr. Tom Giles

Pythagorean Theorem

Use this when you are given 2 sides on a right triangle and need to find the third.
a & b are legs

h is the hypotenuse

45-45-90 (Isosceles)

• If the right triangle has angle measures of 45-45-90, the sides have a pattern.

• To find the length of the hypotenuse, simply multiply the legs by √2

Multiple Choice

In this 45-45-90 triangle, find the hypotenuse x

• x = 4

• x = 4√2

• x = 8

• x = 2

Multiple Choice

In this 45-45-90 triangle, find the other leg y

• y = 4

• y = 4√2

• y = 8

• y = 2

Multiple Choice

In this 45-45-90 triangle, find x

• x = 5

• x = 10

• x = 5√2

• x = 10√2

Multiple Choice

In this 45-45-90 triangle, find y

• y = 5

• y = 10

• y = 5√2

• y = 10√2

30-60-90

• If the right triangle has angle measures of 30-60-90, the sides have a pattern.

• To find the length of the hypotenuse, simply multiply the short leg by 2

• To find the length of the long leg, multiply the short leg by √3

Multiple Choice

I have been given the short leg in this 30-60-90 triangle. How do I find the length of the hypotenuse u?

• Multiply 4 by 2

• Multiply 4 by √3

• Multiply 4 by √2

• Divide 4 by √3

Multiple Choice

I have been given the short leg in this 30-60-90 triangle. How do I find the long leg, y?

• Multiply 4 by 2

• Multiply 4 by √3

• Multiply 4 by √2

• Divide 4 by 2

Multiple Choice

What is the value of y?

• 14

• 7√3

• 7√2

• 7

Multiple Choice

What is the value of x?

• 14

• 7√2

• 7√3

• 7

Multiple Choice

Find y

• 13

• 5

• 23

• 10

Pythagorean Theorem Review

Use this when you are given 2 sides on a right triangle and need to find the third

Multiple Choice

If a right triangle has sides 6, 6.7, and 3, which is c?

• 6

• 6.7

• 3

Multiple Choice

Which equation can be used to find x

• 20² = 14² + x²

• 14² = 20² + x²

• 14² = x² + 20²

• x² = 14² + 20²

Converse of Pythagorean Theorem

• Check if it is a triangle: a+b > c

• If c² < a² + b² --> acute

• If c² = a² + b² --> right

• If c² > a² + b² --> obtuse

Multiple Select

Which three side lengths can form a triangle?

• 3, 8, 4

• 14, 11, 3

• 5, 10, 6

• 4, 5, 10

Multiple Choice

Three side lengths are given below. What type of triangle would they form?

5, 10, 15

• right

• obtuse

• acute

• not a triangle

Multiple Choice

Acute, right, or obtuse?

• Acute

• Right

• Obtuse

• Not a triangle

Multiple Choice

Acute, right, or obtuse?

• Acute

• Right

• Obtuse

• Not a triangle