Pythagorean Theorem and Their Converse

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: a² + b² = c².

Front

What is a right triangle?

Back

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

Front

What is the hypotenuse of a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

If the sides of a triangle are 3, 4, and 5, can it form a right triangle?

Back

Yes, because 3² + 4² = 5² (9 + 16 = 25).

Front

How do you determine if three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths.

Front

What is the converse of the Pythagorean Theorem?

Back

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

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x1, y1) and (x2, y2) in a coordinate plane can be calculated using the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

If a right triangle has legs of lengths 9 and 40, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(9² + 40²) = √(81 + 1600) = √1681 = 41.

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

Can the lengths 6, 8, and 10 form a right triangle?

Back

Yes, because 6² + 8² = 10² (36 + 64 = 100).