Pythagorean Theorem

What is the hypotenuse in a right triangle?

• The shortest side of a right triangle.

• The longest side of a right triangle, opposite the right angle.

• The side adjacent to the right angle.

• The side opposite the longest angle.

What type of triangle does the Pythagorean Theorem apply to?

• Acute triangles

• Obtuse triangles

• Right triangles

• Scalene triangles

What is the formula to find the length of a missing side in a right triangle?

• @@c = ext{sqrt}(a^2 + b^2)@@ (for hypotenuse)

• @@a = ext{sqrt}(c^2 - b^2)@@ (for a leg)

• @@b = ext{sqrt}(c^2 - a^2)@@ (for a leg)

• @@c = a + b@@ (not applicable)

What is the Pythagorean Theorem?

• In a right triangle, the square of the length of the hypotenuse (side 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: @@a^2 + b^2 = c^2@@.

• The sum of the angles in a triangle is equal to 180 degrees.

• The area of a triangle is equal to half the base times the height.

• In a right triangle, the hypotenuse is always the longest side.

What is the converse of the Pythagorean Theorem?

• If a triangle has sides of lengths a, b, and c, and @@a^2 + b^2 = c^2@@, then the triangle is a right triangle.

• If a triangle has sides of lengths a, b, and c, and @@a^2 + b^2 > c^2@@, then the triangle is an acute triangle.

• If a triangle has sides of lengths a, b, and c, and @@a^2 + b^2 < c^2@@, then the triangle is an obtuse triangle.

• If a triangle has sides of lengths a, b, and c, then the sum of the lengths of any two sides is greater than the length of the third side.

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 relationship between the sides of a right triangle according to the Pythagorean Theorem?

• The sum of the squares of the two legs equals the square of the hypotenuse: @@a^2 + b^2 = c^2@@

• The sum of the lengths of the two legs equals the length of the hypotenuse.

• The product of the lengths of the two legs equals the length of the hypotenuse.

• The difference of the squares of the two legs equals the square of the hypotenuse.

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

• It is used to calculate the area of circles.

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

• It helps in determining the speed of light.

• It is primarily used in algebra to solve equations.

What is a leg in a right triangle?

• A leg is the longest side of a right triangle.

• A leg is one of the two shorter sides of a right triangle that form the right angle.

• A leg is the angle opposite the hypotenuse.

• A leg is the sum of the two other sides of the triangle.

If one leg of a right triangle is 6 units and the other leg is 8 units, what is the length of the hypotenuse?

• 8 units

• 10 units

• 12 units

• 14 units