Pythagorean Theorem Review

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 type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem applies only to right triangles.

Front

In a right triangle, which side is the longest?

Back

In a right triangle, the hypotenuse (side c) is always the longest side.

Front

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

Back

Using the Pythagorean Theorem: c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5 cm.

Front

What is the formula to find the distance between two points in a coordinate plane?

Back

The distance formula is derived from the Pythagorean Theorem: d = √((x2 - x1)² + (y2 - y1)²).

Front

How do you find the height of a cone using the Pythagorean Theorem?

Back

If you know the radius and the slant height of the cone, you can use the Pythagorean Theorem: height² + radius² = slant height².

Front

What is the shortest distance back to the starting point if two joggers run 8 miles north and 5 miles west?

Back

Using the Pythagorean Theorem: c² = 8² + 5²; c² = 64 + 25; c² = 89; c = √89 ≈ 9.4 miles.

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 the shortest side is opposite the 30-degree angle.

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 determine if a triangle is a right triangle using side lengths?

Back

You can use the Pythagorean Theorem: if a² + b² = c² holds true for the side lengths, then the triangle is a right triangle.