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 formula to find the length of the hypotenuse in a right triangle?

Back

The formula to find the length of the hypotenuse (c) is: c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

How do you cancel out the square when solving for a side using the Pythagorean Theorem?

Back

You cancel out the square by taking the square root of both sides of the equation.

Front

If one side of a right triangle is 3 ft and the other side is 4 ft, what is the length of the hypotenuse?

Back

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

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, the longer leg is opposite the 60-degree angle, and the hypotenuse is twice the shortest side.

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

How do you round answers to the nearest tenth?

Back

To round to the nearest tenth, look at the hundredths place. If it is 5 or greater, round up the tenths place by one. If it is less than 5, keep the tenths place the same.

Front

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

Back

The Pythagorean Theorem is used in various real-world applications, including construction, navigation, and physics, to determine distances and relationships between different points.

Front

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

Back

To verify 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 it is a right triangle.

Front

What is the area of a right triangle given the lengths of the two legs?

Back

The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height, where the base and height are the lengths of the two legs.