Pythagorean Theorem

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

If a = 5 and b = 12, what is c?

• 10

• 12

• 13

• 15

What is the length of the missing side if one leg is 6 and the hypotenuse is 10?

• 6

• 7

• 8

• 9

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 construction, navigation, and physics to calculate distances and angles.

• It helps in solving quadratic equations.

• It is primarily used in theoretical mathematics.

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

• Yes, because 7² + 24² = 49 + 576 = 625 = 25².

• No, because the longest side is not the hypotenuse.

• Yes, because 7² + 25² = 49 + 625 = 674 = 24².

• No, because 24² + 25² = 576 + 625 = 1201 = 7².

What are Pythagorean Triples?

• Sets of three positive integers that satisfy the Pythagorean Theorem (a² + b² = c²)

• Any three integers that can form a triangle

• Three consecutive integers

• Sets of three negative integers that satisfy the Pythagorean Theorem

How can the Pythagorean Theorem be applied in coordinate geometry?

• To find the area of a triangle formed by three points.

• To determine the slope of a line between two points.

• To calculate the distance between two points using the formula: d = √((x2 - x1)² + (y2 - y1)²).

• To find the midpoint of a line segment between two points.

What type of triangle does the Pythagorean Theorem apply to?

• Equilateral triangles

• Isosceles triangles

• Right triangles

• Scalene triangles

What is the hypotenuse of a right triangle with legs of 9 and 12?

• 12

• 15

• 18

• 21

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 is expressed as a² + b² = c².

• 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.