Special Right Triangle Theorems

What are the two special right triangle theorems?

• Area and perimeter theorem

• Sine and cosine theorem

• Angle sum theorem and exterior angle theorem

• Pythagorean theorem and properties of 45-45-90 and 30-60-90 triangles

What is the formula to find the hypotenuse of a 45-45-90 triangle?

• hypotenuse = a + √2

• hypotenuse = a / √2

• hypotenuse = a * 2

• hypotenuse = a * √2

What is the formula to find the legs of a 45-45-90 triangle?

• leg = hypotenuse + √2

• leg = hypotenuse - √2

• leg = hypotenuse * √2

• The formula to find the legs of a 45-45-90 triangle is leg = hypotenuse / √2

What is the formula to find the hypotenuse of a 30-60-90 triangle?

• Hypotenuse = longer leg - shorter leg

• Hypotenuse = shorter leg / 2

• Hypotenuse = 2 * shorter leg

• Hypotenuse = shorter leg + longer leg

What is the formula to find the short leg of a 30-60-90 triangle?

• Short leg = (Hypotenuse) - (1/2)

• Short leg = (Hypotenuse) + (1/2)

• Short leg = (Hypotenuse) * (2)

• Short leg = (Hypotenuse) * (1/2)

What is the formula to find the long leg of a 30-60-90 triangle?

• Long leg = short leg + √3

• Long leg = short leg / √3

• Long leg = short leg - √3

• Long leg = short leg * √3

In a 45-45-90 triangle, if the legs are 5 units each, what is the length of the hypotenuse?

• 5√2 units

• 10 units

• 5 units

• 7.5 units

In a 30-60-90 triangle, if the short leg is 4 units, what is the length of the long leg?

• 4√2 units

• 16 units

• 8 units

• 4√3 units

In a 30-60-90 triangle, if the long leg is 10 units, what is the length of the short leg?

• 5 units

• 3 units

• 15 units

• 8 units

In a 45-45-90 triangle, if the hypotenuse is 12 units, what is the length of each leg?

• Each leg is 12 + √2 units

• Each leg is 12 * √2 units

• Each leg is 12 - √2 units

• Each leg is 12 / √2 units