Pythagorean Theorem (Missing Sides)

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 is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

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

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

How do you find a missing side of a right triangle when the hypotenuse and one side are known?

Back

Use the Pythagorean Theorem: c² = a² + b². Rearrange to find the missing side: a = √(c² - b²) or b = √(c² - a²).

Front

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

Back

The formula is derived from the Pythagorean Theorem: a² + b² = c².

Front

If the hypotenuse is 10 and one side is 6, what is the length of the other side?

Back

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

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 check if a triangle is a right triangle using the Pythagorean Theorem?

Back

If a² + b² = c² holds true for the lengths of the sides, then the triangle is a right triangle.