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

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem applies only to right triangles.

Front

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

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100, so c = √100 = 10 units.

Front

What is the formula for finding the hypotenuse in a right triangle?

Back

The formula for finding the hypotenuse is a² + b² = c².

Front

In the context of the Pythagorean Theorem, what do the letters a, b, and c represent?

Back

In the Pythagorean Theorem, 'a' and 'b' represent the lengths of the two legs of the right triangle, while 'c' represents the length of the hypotenuse.

Front

How can the Pythagorean Theorem be used in real-life applications?

Back

The Pythagorean Theorem can be used in various real-life applications such as construction, navigation, and determining distances between points.

Front

If a right triangle has a hypotenuse of 13 units and one leg of 5 units, what is the length of the other leg?

Back

Using the Pythagorean Theorem: c² = a² + b², so 13² = 5² + b². This gives 169 = 25 + b², thus b² = 144, and b = 12 units.

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, where the shortest side is opposite the 30-degree angle.

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 do you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if the squares of the lengths of the two shorter sides add up to the square of the length of the longest side.