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: c² = a² + b².

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

Back

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

Front

Which type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

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

Back

8 (Using the Pythagorean Theorem: 6² + b² = 10², so 36 + b² = 100, thus b² = 64, and b = √64 = 8).

Front

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

Back

c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

Front

In a right triangle, if the lengths of the legs are both equal, what type of triangle is it?

Back

It is an isosceles right triangle.

Front

How do you determine if a triangle is a right triangle using side lengths?

Back

If the square of the longest side equals the sum of the squares of the other two sides, then it is a right triangle (c² = a² + b²).

Front

What is the relationship between the angles and sides in a right triangle?

Back

The side opposite the largest angle (90 degrees) is the hypotenuse, and it is always the longest side.

Front

If a ladder is placed 10 feet away from a wall and reaches a height of 24 feet, how long is the ladder?

Back

26 feet (Using the Pythagorean Theorem: 10² + 24² = c², so 100 + 576 = c², thus c = √676 = 26).