Скачать или смотреть Pythagorean theorem - SAT Math

*CORE CONCEPT*
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse length is equal to the sum of the squares of the other two sides.

*TOPICS COVERED*
When to use the Pythagorean theorem to find missing side lengths in right triangles (B2)
How to apply the theorem to solve real-world problems involving right triangles (B2)
When to identify right triangles and label sides as a, b, and c (B2)

*EXAMPLE SENTENCES*
Example 1: Find the length of the hypotenuse in a right triangle with legs of length 3 and 4.
Example 2: A ladder leans against a wall, forming a right triangle with the ground. If the ladder is 10 feet long and the base is 6 feet from the wall, find the height of the wall.
Example 3: A rectangular garden has a length of 8 meters and a width of 6 meters. Find the diagonal length.

*GRAMMAR RULES*
Identify the right triangle → Ensure the triangle has a right angle (90 degrees) and label the sides as a, b (legs), and c (hypotenuse).
Use the Pythagorean theorem → Apply the formula a² + b² = c² to find the length of a missing side.
Solve and interpret → Calculate the missing side length and interpret the result in the context of the problem.

*COMMON ERRORS*
Wrong: For a triangle with legs 5 and 12, calculating the hypotenuse as 5 + 12 = 17. → Right: For a triangle with legs 5 and 12, calculating the hypotenuse correctly as 5² + 12² = 13.
Wrong: For a right triangle with legs 9 and 12, finding the hypotenuse as 9² + 12 = 144. → Right: For a right triangle with legs 9 and 12, finding the hypotenuse correctly as 9² + 12² = 15.

*STUDENT QUESTIONS*
How do I use the Pythagorean theorem?
When to apply the Pythagorean theorem in real-world problems?
Is this example of the Pythagorean theorem correct?
What's the difference between hypotenuse and legs in a triangle?
How do I find the missing side length using the theorem?

*KEY CONCEPTS*
Pythagorean theorem, right triangle, hypotenuse, side lengths, B2 level, geometry concepts.

Key concepts (auto-augmented): pythagorean theorem a^2 + b^2 = c^2, soh cah toa trigonometry, special right triangles 30-60-90