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 one leg of a right triangle is 5 units and the other leg is 12 units, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 5² + 12²; c² = 25 + 144; c² = 169; c = 13 units.

Front

What is the relationship between the areas of squares constructed on the sides of a right triangle?

Back

The sum of the areas of the squares on the two legs of a right triangle is equal to the area of the square on the hypotenuse.

Front

In a right triangle, if one leg is 7 units and the hypotenuse is 18 units, how do you find the other leg?

Back

Use the Pythagorean Theorem: a² + 7² = 18²; a² + 49 = 324; a² = 275; a ≈ 16.6 units.

Front

What is the formula to find the area of a square?

Back

The area of a square is calculated as A = side², where 'side' is the length of one side of the square.

Front

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

Back

It is an isosceles right triangle.

Front

What is the value of the hypotenuse if both legs of a right triangle are 1 unit long?

Back

Using the Pythagorean Theorem: c² = 1² + 1²; c² = 1 + 1; c² = 2; c = √2 ≈ 1.41 units.

Front

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

Back

Use the Pythagorean Theorem: If a² + b² = c² holds true for the side lengths, then the triangle is a right triangle.

Front

What happens to the hypotenuse if both legs of a right triangle are increased?

Back

The hypotenuse will also increase, as it is dependent on the lengths of the legs.