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 is expressed as: a² + b² = c².

Front

Is the statement 'a² + b³ = c⁴' true or false?

Back

False. The correct formula is a² + b² = c².

Front

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

Back

The formula is c = √(a² + b²).

Front

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

Back

c = √(6² + 8²) = √(36 + 64) = √100 = 10.

Front

In a right triangle, which side is always the longest?

Back

The hypotenuse (side c) is always the longest side.

Front

If a = 3 and b = 4, what is c?

Back

c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What does it mean if a triangle does not satisfy the Pythagorean Theorem?

Back

If a² + b² < c², the triangle is obtuse. If a² + b² > c², the triangle is acute.

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

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

Back

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