Multiplying Binomials with FOIL
9-12
2
The Pythagorean Theorem
Lesson Details
Grade Level
9-12
Duration (minutes)
1
Summary
A Grade 9-12 math lesson teaching students how to use the Pythagorean theorem (a² + b² = c²) to find a missing side length in a right triangle, with worked examples solving for both the hypotenuse and a missing leg.
Student Worksheet: The Pythagorean Theorem
Teacher Note: Students can watch the video lesson above and answer the questions. Click the “Teacher Answer Key” dropdown below when you are ready to review the solutions!
Key Concepts:
• Right Triangle Parts: The hypotenuse is the side opposite the 90° angle and is always the longest side; the other two sides are called legs.
• The Formula: a² + b² = c², where a and b are the legs and c is the hypotenuse.
• Finding the Hypotenuse: If you know both legs, square each one, add them together, then take the square root of the sum.
• Finding a Missing Leg: If you know the hypotenuse and one leg, substitute into the formula and solve for the missing squared value before taking the square root.
Instructions: Read each question carefully and write your answer in the space provided.
- Question 1: What is the Pythagorean theorem formula, and what does each letter represent?
- Question 2: A right triangle has legs of length 3 and 4. Find the hypotenuse. Show your steps.
- Question 3: Why is the hypotenuse always the longest side of a right triangle?
- Question 4: A right triangle has a hypotenuse of 13 and one leg of 5. Find the missing leg. Show your steps.
- Question 5: In Question 4, why do you subtract 25 from 169 instead of adding?
Click to reveal Teacher Answer Key
1. a² + b² = c², where a and b are the legs and c is the hypotenuse.
2. 3² + 4² = c². 9 + 16 = 25 = c². c = √25 = 5.
3. It is opposite the 90° angle, which is the largest angle in a right triangle, so the side across from it is always the longest.
4. a² + 5² = 13². a² + 25 = 169. a² = 144. a = √144 = 12.
5. Because you need to isolate a² alone on one side of the equation, so you subtract 25 from both sides instead of adding.
Disclaimer: This worksheet was generated with AI assistance based on original video content. It is intended for educational reference only. Teachers are encouraged to review and adjust questions to fit their curriculum standards before classroom use.
🎯 Extension Activity: A right triangle has legs of length 6 and 8. Find the hypotenuse. Then, using a hypotenuse of 10 and one leg of 6, find the missing leg. Show every step for both.