Pythagoras 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 is the hypotenuse in a right triangle?

Back

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

Front

What are the legs of a right triangle?

Back

The legs are the two sides that form the right angle in a right triangle.

Front

How do you find the length of a leg if you know the hypotenuse and the other leg?

Back

You can use the formula: c² - a² = b², where c is the hypotenuse, a is the known leg, and b is the leg you want to find.

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

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

Front

What is the formula to calculate the area of a right triangle?

Back

The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height.

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

Back

Using the formula: c² - a² = b², we have 10² - 6² = b², so 100 - 36 = b², thus b² = 64, and b = 8.

Front

What is the converse of the Pythagorean Theorem?

Back

The converse states that if a triangle has sides of lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.