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 are the conditions for a triangle to be a right triangle?

Back

A triangle is a right triangle if one of its angles measures 90 degrees. This can be verified using the Pythagorean Theorem.

Front

If a right triangle has legs of lengths 3 and 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?

Back

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

Front

How can you determine if a set of three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths.

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. 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

If one leg of a right triangle is 12 cm and the hypotenuse is 13 cm, what is the length of the other leg?

Back

Using the Pythagorean Theorem: 12² + b² = 13²; 144 + b² = 169; b² = 25; b = 5 cm.

Front

What is the area of a right triangle with a base of 10 cm and a height of 6 cm?

Back

Area = (1/2) * base * height = (1/2) * 10 * 6 = 30 cm².

Front

What is the formula for the perimeter of a right triangle?

Back

The perimeter of a right triangle is the sum of the lengths of all three sides: P = a + b + c.