Pythagorean Theorem and Their Converse

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

• It is used in construction, navigation, and various fields to calculate distances.

• It is primarily used in algebra to solve equations.

• It is a theorem that only applies to theoretical mathematics.

• It is used to calculate the area of circles.

Which is the Pythagorean theorem?

• c² = a² + b²

• a² + b² = c

• c = a + b

• c² = a² - b²

What type of triangle does the Pythagorean Theorem apply to?

• Acute triangle

• Obtuse triangle

• Right triangle

• Scalene triangle

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

• 1:1:√2

• 1:2:√3

• 2:2:√2

• 1:1:1

What is the formula to find the length of a leg in a right triangle if the hypotenuse and one leg are known?

• a = √(c² - b²) or b = √(c² - a²)

• a = c² + b²

• b = c² - a²

• a = c - b

If a right triangle has a hypotenuse of 25 and one leg of 24, what is the length of the other leg?

• 5

• 12

• 7

• 10

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

If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

• Yes, because 5² + 12² = 13².

• No, because the sides do not satisfy the Pythagorean theorem.

• Yes, but only if the triangle is isosceles.

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

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

• 1:1:1

• 1:√2:2

• 1:√3:2

• 1:2:√3

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

• 6

• 7

• 8

• 9