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: 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 find the length of a missing side in a right triangle?

Back

To find the length of a missing side in a right triangle, use the Pythagorean Theorem. If you know the lengths of the other two sides, rearrange the formula to solve for the missing side.

Front

If one side of a right triangle is 6 in and the other is 8 in, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10 in.

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° angle is the shortest, the side opposite the 60° angle is √3 times the shortest side, 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 length of the hypotenuse is √2 times the length of one leg.

Front

How can the Pythagorean Theorem be applied in real-life situations?

Back

The Pythagorean Theorem can be used in various real-life situations, such as determining the distance between two points, calculating heights of objects, and in construction to ensure structures are level.

Front

What is the significance of the Pythagorean Theorem in geometry?

Back

The Pythagorean Theorem is fundamental in geometry as it establishes a relationship between the sides of right triangles, which is essential for solving many geometric problems.

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem specifically applies to right triangles. For non-right triangles, other methods such as the Law of Cosines or the Law of Sines are used.

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if a triangle has sides of lengths a, b, and c, and if a² + b² = c², then the triangle is a right triangle.