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 is expressed as a² + b² = c².

Front

What does 'h' represent in the context of the Pythagorean Theorem?

Back

In the context of the Pythagorean Theorem, 'h' typically represents the length of the hypotenuse of a right triangle.

Front

How do you find the length of a missing side in a right triangle using the Pythagorean Theorem?

Back

To find the length of a missing side, rearrange the Pythagorean Theorem formula. If you know the lengths of the other two sides, use a² + b² = c² to solve for the unknown side.

Front

If one side of a right triangle is 80 inches and the other side is 60 inches, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(80² + 60²) = √(6400 + 3600) = √10000 = 100 inches.

Front

What is the scale factor in similar triangles?

Back

The scale factor is the ratio of the lengths of corresponding sides of two similar triangles.

Front

If the scale factor from a small triangle to a large triangle is 2, what does this mean?

Back

It means that each side of the large triangle is twice the length of the corresponding side of the small triangle.

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, where 1 is the length of the side opposite the 30-degree angle, √3 is opposite the 60-degree angle, and 2 is the hypotenuse.

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 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 length of the longest side equals the sum of the squares of the lengths of the other two sides.

Front

What is the formula for calculating the area of a right triangle?

Back

The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height.