Pythagorean Theorem

Front

What is the Pythagorean Theorem?

Back

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: a² + b² = c².

Front

What are the conditions for a triangle to be a right triangle?

Back

A triangle is a right triangle if one of its angles measures 90 degrees. This can be verified using the Pythagorean Theorem.

Front

If a triangle has sides of lengths 9, 12, and 15, does it form a right triangle?

Back

Yes, because 9² + 12² = 15² (81 + 144 = 225).

Front

What is the length of the hypotenuse if the other two sides are 35 and 60?

Back

Using the Pythagorean Theorem: c = √(35² + 60²) = √(1225 + 3600) = √4825 ≈ 69.5.

Front

Which set of sides forms a right triangle: 4, 5, 6 or 5, 12, 13?

Back

5, 12, 13 forms a right triangle because 5² + 12² = 13² (25 + 144 = 169).

Front

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

Back

To find a missing side, use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

If one side of a right triangle is 16 inches and the hypotenuse is 80 inches, what is the length of the other side?

Back

Using the Pythagorean Theorem: b = √(80² - 16²) = √(6400 - 256) = √6144 ≈ 78.4 inches.

Front

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

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Front

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

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

How can you verify if a triangle with sides 8, 15, and 17 is a right triangle?

Back

Check if 8² + 15² = 17². If true, it is a right triangle: 64 + 225 = 289.