Pythagorean Theorem - End of Unit

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

If a = 12 and b = 35, what is c?

Back

c = 37, since 12² + 35² = 144 + 1225 = 1369, and √1369 = 37.

Front

Do the sides 6 mi, 14 mi, and 17 mi form a right triangle?

Back

No, because 6² + 14² = 36 + 196 = 232, which is not equal to 17² (289).

Front

Find the missing side if a = 4 and b = 16. What is c?

Back

c = √(4² + 16²) = √(16 + 256) = √272 = 16.49.

Front

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

Back

Yes, because 15² + 20² = 225 + 400 = 625, which equals 25² (625).

Front

What is the distance formula?

Back

The distance formula is used to find the distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane: d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

Calculate the distance between the points (-5, 3) and (4, -5).

Back

Distance = √((4 - (-5))² + (-5 - 3)²) = √(9² + (-8)²) = √(81 + 64) = √145 = 12.04.

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

What is the hypotenuse of a right triangle?

Back

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