Pythagorean Review 2

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 is a Pythagorean Triple?

Back

A Pythagorean Triple consists of three positive integers (a, b, c) that satisfy the equation a² + b² = c². Examples include (3, 4, 5) and (5, 12, 13).

Front

Is the set of numbers 10, 24, 26 a Pythagorean Triple?

Back

Yes, because 10² + 24² = 100 + 576 = 676, which is equal to 26².

Front

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

Back

To find the length of the missing side in a right triangle, use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

Can a triangle with side lengths 4, 5, and 6 be a right triangle?

Back

No, because 4² + 5² = 16 + 25 = 41, which is not equal to 6² (36).

Front

What is the length of the hypotenuse if one side is 5 and the other side is 12?

Back

Using the Pythagorean Theorem: c = √(5² + 12²) = √(25 + 144) = √169 = 13.

Front

What does it mean for a triangle to be a right triangle?

Back

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

Front

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

Back

You can determine if a triangle is a right triangle by checking if the square of the longest side is equal to the sum of the squares of the other two sides.

Front

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

Back

In a right triangle, the side opposite the right angle is the hypotenuse, and it is the longest side.

Front

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

Back

The Pythagorean Theorem is used in various fields such as architecture, construction, and navigation to calculate distances and ensure structures are built correctly.