Understanding the Theorem
This theorem applies to what type of triangle?
What is a right triangle?
If one leg of a right triangle is 3 units and the other is 4 units, this is the length of the hypotenuse.
What is 5 units?
$100: The Pythagorean Theorem helps find distances in this real-world coordinate system.
What is the Cartesian coordinate system (or the coordinate plane)?
A ladder 10 feet long leans against a wall, reaching 8 feet high. This is the distance of the ladder's base from the wall.
What is 6 feet?
This term describes a set of three positive integers that satisfy the Pythagorean Theorem.
What is a Pythagorean triple?
The Pythagorean Theorem is used to find the length of this side, given the lengths of the other two sides.
What is the hypotenuse?
The length of one leg is 6 and the hypotenuse is 10. This is the length of the other leg.
What is 8 units?
$200: This construction tool helps achieve perfect corner angles, often using the Pythagorean Theorem.
What is a square or carpenter's square?
A rectangular garden has a width of 7 units and a diagonal of 25 units. This is the length of the garden.
What is 24 units?
Often used in architecture, this Pythagorean triple is defined by 3, 4, and this number.
What is 5?
The theorem states that the square of the hypotenuse is equal to the sum of the squares of these two sides.
What are the legs?
A right triangle has legs of length 5 and 12. This is the length of the hypotenuse.
What is 13 units?
This is a common use of the Pythagorean Theorem for determining diagonal lengths in rectangles and squares.
What is calculating the diagonal of a TV or screen size?
A car drives 3 miles north and then 4 miles east. This is how far the car is from the starting point.
What is 5 miles?
Besides the common triples like (3, 4, 5), these two numbers also form a Pythagorean triple with 13.
What are 5 and 12?
Name the ancient Greek mathematician credited with formulating the Pythagorean Theorem.
Who is Pythagoras?
This is the missing leg length in a triangle where the hypotenuse is 17 and one leg is 8.
What is 15 units?
When architects design these structures, they often use the Pythagorean Theorem to ensure stability and form.
What are bridges?
$400: In a park, a straight path diagonally crosses a rectangular field measuring 16 by 30 yards. This is the path's length.
What is 34 yards?
This term refers to the process of using irrational numbers in the calculation of hypotenuse length in non-integer right triangles.
What is square rooting or radical expressions?
This is the mathematical representation of the theorem.
What is a² + b² = c²?
For a triangle with a leg of 9 and hypotenuse of 12, this is the length of the other leg. Round to the tenths place.
What is 7.9 units?
$500: Astronomers apply the Pythagorean Theorem in calculations involving distances in this realm.
What is outer space or astronomical measurements?
A sailboat sails 5 km east and then 12 km directly north. This is the shortest distance back to the starting point.
What is 13 km?
The extension of the Pythagorean Theorem into higher-dimensional spaces is known as this.
What is the extended version or generalized Pythagorean Theorem?