Exploring the Pythagorean Theorem and Special Right Triangles

What is a Pythagorean triple?

• A set of three natural numbers that satisfy the equation a^2 + b^2 = c^2.

• A formula to calculate the area of a triangle.

• A type of triangle where all sides are equal.

• A method to determine the height of a pyramid.

Which of the following is a common example of a Pythagorean triple?

• 1, 2, 3

• 5, 5, 5

• 2, 3, 4

• 3, 4, 5

How do you calculate the diagonal of a box using the Pythagorean theorem?

• Add the squares of the length and width.

• Subtract the square of the height from the sum of the squares of the length and width.

• Multiply the length by the width and take the square root.

• Add the squares of the length, width, and height and take the square root.

What does the Hinge Theorem state about the sides and angles of a triangle?

• The largest angle is opposite the longest side.

• All angles are equal if all sides are equal.

• The longest side is opposite the smallest angle.

• The smallest angle is opposite the longest side.

What are the side lengths of a 45-45-90 triangle if the hypotenuse is 1?

• 1, 1, 1

• sqrt(2)/2, sqrt(2)/2, 1

• 1/sqrt(2), 1/sqrt(2), 1

• 0.5, 0.5, 1

In a 30-60-90 triangle, if the shortest side is 1, what is the length of the hypotenuse?

• 1

• 3

• 2

• sqrt(3)

Which statement is true about the sides of a right triangle?

• The hypotenuse is the shortest side.

• The hypotenuse is perpendicular to the base.

• The side opposite the right angle is called the hypotenuse.

• All sides are of equal length.

What is the correct side ratio for a 30-60-90 triangle?

• 1:1:1

• 1:2:3

• 1:2:sqrt(3)

• 1:sqrt(3):2

What can be inferred about a triangle with angles in the ratio 1:2:3?

• It cannot be determined from the ratio alone.

• It is an isosceles triangle.

• It is an equilateral triangle.

• It is a right triangle.

What is the side length opposite the smallest angle in a triangle with side ratios 1:2:3 and the smallest side being 12?

• 36

• 24

• 12

• 48