The Pythagorean Theorem

What is the converse of the Pythagorean Theorem?

• If a triangle has sides of lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.

• If a triangle is a right triangle, then a² + b² = c².

• If a triangle has sides of lengths a, b, and c, and a² + b² > c², then the triangle is obtuse.

• If a triangle has sides of lengths a, b, and c, and a² + b² < c², then the triangle is acute.

What is the Pythagorean Theorem?

• The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².

• The Pythagorean Theorem states that the sum of the angles in a triangle is 180 degrees.

• The Pythagorean Theorem states that in any triangle, the longest side is always opposite the largest angle.

• The Pythagorean Theorem states that the area of a triangle is equal to half the base times the height.

What type of triangle does the Pythagorean Theorem apply to?

• Equilateral triangles

• Isosceles triangles

• Right triangles

• Scalene triangles

If one side of a right triangle is 5 and the other side is 12, what is the length of the hypotenuse?

• 10

• 12

• 13

• 15

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

• The lengths of the legs are equal, and the hypotenuse is √2 times the length of a leg.

• The lengths of the legs are equal, and the hypotenuse is twice the length of a leg.

• The hypotenuse is equal to the sum of the lengths of the legs.

• The lengths of the legs are half the length of the hypotenuse.

What is a right triangle?

• A triangle that has one angle measuring 90 degrees.

• A triangle with all sides of equal length.

• A triangle that has no angles measuring 90 degrees.

• A triangle that has two angles measuring 45 degrees.

What is the square root of 144?

• 10

• 11

• 12

• 13

What is the relationship between the sides of a 30-60-90 triangle?

• 1:2:3

• 1:√2:2

• 1:√3:2

• 1:√4:2

What is the significance of the Pythagorean Theorem in real life?

• It is primarily used in cooking to measure ingredients.

• It is used in various fields such as architecture, construction, navigation, and physics to calculate distances and angles.

• It helps in determining the best routes for public transportation.

• It is mainly applicable in the field of literature for analyzing texts.

What is the opposite of squaring a number?

• Taking the square root

• Cubing the number

• Adding the number to itself

• Subtracting the number from one