5.5 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

How can you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides. If c² = a² + b² holds true, then the triangle is a right triangle.

Front

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

Back

To find the length of a missing side in a right triangle, use the Pythagorean Theorem: c² = a² + b². Rearrange the formula to solve for the missing side.

Front

In a right triangle with sides 3, 4, and 5, which side is the hypotenuse?

Back

The hypotenuse is the longest side, which is 5.

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 side opposite the 30-degree angle is the shortest, the side opposite the 60-degree angle is √3 times the shortest side, and the hypotenuse is twice the shortest side.

Front

What is the opposite of squaring a number?

Back

The opposite of squaring a number is taking the square root of that number.

Front

If a right triangle has side lengths of 6, 8, and x, how do you find x?

Back

Use the Pythagorean Theorem: x² = 6² + 8². Calculate x = √(36 + 64) = √100 = 10.

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle and is opposite the right angle. It is crucial for applying the Pythagorean Theorem.

Front

How do you 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 a common application of the Pythagorean Theorem in real life?

Back

The Pythagorean Theorem is commonly used in construction, navigation, and various fields of engineering to determine distances and create right angles.