Pythagorean Theorem and Right Triangles

What is a right triangle?

• A triangle with all angles measuring less than 90 degrees.

• A triangle that has one angle measuring 90 degrees.

• A triangle with two equal sides.

• A triangle that has no equal sides.

If the hypotenuse of a right triangle is 10 and one leg is 6, what is the length of the other leg?

• 6

• 8

• 10

• 12

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.

If a right triangle has legs of lengths 5 and 12, what is the length of the hypotenuse?

• 10

• 12

• 13

• 15

How do you find the length of a missing side in a right triangle?

• Use the Pythagorean Theorem: @@a^2 + b^2 = c^2@@, where c is the hypotenuse.

• Multiply the lengths of the other two sides.

• Add the lengths of the other two sides.

• Use the formula for the area of the triangle.

If one leg of a right triangle is 3 and the other leg is 4, what is the length of the hypotenuse?

• 4

• 5

• 6

• 7

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

• It is used to calculate the area of triangles.

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

• It helps in solving quadratic equations.

• It is primarily used in theoretical mathematics.

How can the Pythagorean Theorem be applied to find distances on a coordinate plane?

• To find the distance between two points (x1, y1) and (x2, y2) on a coordinate plane, use the formula: @@d = ext{√}((x2 - x1)^2 + (y2 - y1)^2)@@.

• To calculate the area of a triangle formed by the points (x1, y1), (x2, y2), and the origin.

• To determine the slope of the line connecting two points (x1, y1) and (x2, y2).

• To find the midpoint between two points (x1, y1) and (x2, y2).

What is the hypotenuse of a right triangle?

• The side opposite the right angle and the longest side of the triangle.

• The side adjacent to the right angle.

• The shortest side of the triangle.

• The angle opposite the longest side.

What is the Pythagorean Theorem?

• 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: @@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 length of the hypotenuse is always greater than the lengths of the other two sides.