Exploring Special Right Triangles

What does having two equal angles in a triangle imply about its sides?

• The sides opposite the equal angles are also equal.

• The sides form an arithmetic sequence.

• The sides are all different lengths.

• The triangle is always obtuse.

In a 45-45-90 triangle, if one leg is 8 units, what is the length of the hypotenuse?

• 16 units

• 8√2 units

• 8 units

• 4√2 units

What is the relationship between the legs of a 45-45-90 triangle?

• They are congruent.

• One is double the other.

• They are perpendicular.

• They form a linear pair.

How do you label the sides of a 30-60-90 triangle?

• X, X, X√2

• X, 2X, X√3

• X, X√3, 2X

• 2X, X, X√3

In a 30-60-90 triangle, if the hypotenuse is 20 units, what is the length of the longer leg?

• 10√3 units

• 10 units

• 20√3 units

• 5√3 units

How is the hypotenuse of a 30-60-90 triangle related to its shortest leg?

• It is triple the length.

• It is double the length.

• It is equal in length.

• It is half the length.

If the longer leg of a 30-60-90 triangle measures 21 units, what is the length of the hypotenuse?

• 21/√3 units

• 42 units

• 14 units

• 21√3 units

In a 30-60-90 triangle, if the longer leg is 14√3, what is the length of the shortest leg?

• 14 units

• 14√3 units

• 7 units

• 28 units

If the hypotenuse of a 45-45-90 triangle is 32√2, what is the length of one leg?

• 32 units

• 16 units

• 64 units

• 32√2 units

When solving a double triangle problem involving a 45-45-90 triangle and a 30-60-90 triangle, what is the first step?

• Label all sides of both triangles.

• Identify the type of each triangle.

• Solve the 45-45-90 triangle first.

• Solve the 30-60-90 triangle first.