🔑 Key Concepts
- Pythagorean theorem word problems often describe a right triangle in a real-world situation.
- Vertical distances and horizontal distances usually form the two legs of the right triangle.
- The slanted object, such as a ladder or a diagonal distance, is usually the hypotenuse.
- When the square root is not a whole number, use a calculator and round as directed.
- Rounding to the nearest tenth means keeping one digit after the decimal point.
✏️ Worked Examples
🧠 Math Vocabulary
- Pythagorean Theorem: A rule for right triangles that states \(a^2+b^2=c^2\).
- Right Triangle: A triangle with one \(90^\circ\) angle.
- Hypotenuse: The longest side of a right triangle, located across from the right angle.
- Legs: The two sides of a right triangle that form the right angle.
- Horizontal Distance: A side-to-side distance, usually along the ground.
- Vertical Distance: An up-and-down distance, such as height or rise.
- Nearest Tenth: A rounded value with one digit after the decimal point.
- Approximation: A value that is close to the exact answer, often shown with \(\approx\).
💡 Main Idea
In this lesson, students solve real-world Pythagorean theorem word problems where the answer is not a perfect square. They learn how to identify the legs and hypotenuse, find the square root, and round the answer to the nearest tenth.
📚 What You Should Already Know
Students should know how to identify right triangles, square numbers, find square roots with a calculator, recognize the hypotenuse, and round decimals to the nearest tenth.
🚀 What Comes Next
After solving these problems, students can apply the Pythagorean theorem to maps, diagonal measurements, coordinate plane distance, ramp problems, and other real-world geometry situations.
🧩 Embed This Video in Your LMS
Teachers can embed this YouTube video directly into Canvas, Google Classroom, Schoology, or another learning platform. Click below to show the embed code for this video.