Pythagorean Theorem Flashcard

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 a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What is the hypotenuse in a right triangle?

Back

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

Front

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

Back

To determine if three sides can form a right triangle, apply the Pythagorean Theorem: check if a² + b² = c², where c is the longest side.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the hypotenuse is always longer than either of the other two sides.

Front

If the sides of a right triangle are 3 and 4, what is the length of the hypotenuse?

Back

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

Front

What is the formula to find the length of a missing side in a right triangle?

Back

To find the length of a missing side, rearrange the Pythagorean Theorem: if c is the hypotenuse, then a = √(c² - b²) or b = √(c² - a²).

Front

In the context of the Pythagorean Theorem, what does 'c' represent?

Back

In the Pythagorean Theorem, 'c' represents the length of the hypotenuse.

Front

What is the significance of the Pythagorean Theorem in real-life applications?

Back

The Pythagorean Theorem is used in various real-life applications, such as construction, navigation, and determining distances.

Front

How do you calculate the height reached by a ladder leaning against a wall?

Back

Use the Pythagorean Theorem: if the ladder is the hypotenuse (c) and the distance from the wall is one side (a), then the height (b) can be found using b = √(c² - a²).