Hypotenuse Leg Theorems

Are these triangles congruent?

• Yes, by AAS

• Yes, by SAS

• Yes, by ASA

• No, this is the SSA one!!

Answer explanation

Even though Side-Side-Angle are marked congruent, SSA is NOT a triangle congruence theorem.

This cannot prove triangles are congruent.

Remember "No swearing!"

In this 45-45-90 triangle, I have been given the length of a leg.  How do I find the length of the hypotenuse?

• It is the same length as the given leg.

• Multiply that leg's length by √2.

• Multiply that leg's length by 2.

• Divide that leg's length by √2.

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

• Multiply 4 by 2

• Multiply 4 by √3

• Multiply 4 by √2

• Divide 4 by √3

What is the length of x in this 45-45-90 triangle?

• 4√2

• 4

• 8

• 4√3

What is the length of y in this 45-45-90 triangle?

• 8√2

• 4√2

• 4

• 8

What is the length of u and v in this 30-60-90 triangle?

• u = 8 v = 4√3

• u = 4√2 v = 8

• u = 16 v = 8

• u = 4√3 v = 8

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

• Divide 8 by √3

• Divide 8 by 2

• Divide 8 by 2, then multiply that answer by √2

• Divide 8 by √3, then multiply that answer by 2

What are x and y in this 30-60-90 triangle?

• x = 6 y = 3√3

• x = 1.5√3 y =1.5

• x = 3√3 y = 6

• x = √3 y = 2√3

What are x and y in this 30-60-90 triangle?

• x = 6 y = 3√3

• x = 3√2 y = 3

• x = 3√3 y = 6

• x = 3√3 y = 3√2

You are making a guitar pick that resembles an equilateral triangle with side lengths of 32 millimeters. What is the approximate height of the pick? (hint: use 30-60-90 theorems)

• 32√3

• 16√3

• 32

• 16√2