8.7C 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 is the hypotenuse in a right triangle?

Back

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

Front

If a right triangle has sides of lengths 6, 6.7, and 3, which side is the hypotenuse?

Back

6.7

Front

Does the set of numbers 20, 25, and 15 represent a right triangle?

Back

Yes

Front

What is the formula used to solve for the hypotenuse in a right triangle?

Back

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 are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle.

Front

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

Back

You can use the Pythagorean Theorem: if a² + b² = c², where c is the longest side, then the lengths can form 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 is given by: d = √((x2 - x1)² + (y2 - y1)²).

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

5 (since 3² + 4² = 9 + 16 = 25, and √25 = 5).