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 type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

If one side of a right triangle is 3 and the other side is 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 3² + 4² = c²; 9 + 16 = c²; 25 = c²; c = 5.

Front

What is the hypotenuse in a right triangle with sides 5 and 12?

Back

Using the Pythagorean Theorem: 5² + 12² = c²; 25 + 144 = c²; 169 = c²; c = 13.

Front

How do you find the length of a missing side in a right triangle?

Back

To find a missing side, rearrange the Pythagorean Theorem: a² + b² = c². If you know two sides, solve for the third.

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

If a right triangle has a hypotenuse of 10 and one side of 6, what is the length of the other side?

Back

Using the Pythagorean Theorem: 6² + b² = 10²; 36 + b² = 100; b² = 64; b = 8.

Front

What is the formula to calculate the diagonal of a rectangle?

Back

The diagonal (d) can be calculated using the Pythagorean Theorem: d = √(length² + width²).

Front

In a right triangle, if one angle is 90 degrees, what are the other two angles?

Back

The other two angles in a right triangle must add up to 90 degrees.