Pythagorean Theorem

Front

What are the 2 shorter sides of a right triangle called?

Back

Legs

Front

What is the Pythagorean Theorem?

Back

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). This is expressed as: a² + b² = c².

Front

What is the hypotenuse in a right triangle?

Back

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

Front

Can side lengths 3, 4, and 5 form a right triangle?

Back

Yes, because 3² + 4² = 5² (9 + 16 = 25).

Front

Do the segment lengths 9, 12, and 18 form a right triangle?

Back

No, because 9² + 12² ≠ 18² (81 + 144 ≠ 324).

Front

Which equation can be used to solve for 'x' in a right triangle?

Back

21² – 15² = x².

Front

What is the formula to find the length of the hypotenuse?

Back

c = √(a² + b²) where c is the hypotenuse and a and b are the legs.

Front

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

Back

10 (using the Pythagorean theorem: 6² + 8² = c², 36 + 64 = 100, c = √100 = 10).

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 a leg.