Florida Standards
- MA.8.GR.1.1 - Apply the Pythagorean Theorem to solve mathematical and real-world problems involving unknown side lengths in right triangles.
What You'll Learn Today:
1
Identify the legs and hypotenuse of a right triangle
2
Use the Pythagorean Theorem to find the hypotenuse
3
Use the Pythagorean Theorem to find a missing leg
The Pythagorean Theorem
a² + b² = c²
In a right triangle, the sum of the squares of the two legs (a and b) equals the square of the hypotenuse (c).
Finding the Hypotenuse
When you know both legs (a and b):
c = √(a² + b²)
The hypotenuse is ALWAYS the longest side!
Finding a Leg
When you know the hypotenuse (c) and one leg:
a = √(c² - b²)
Subtract the known leg² from hypotenuse²
Key Points to Remember
1
The hypotenuse is always opposite the right angle (the longest side)
2
The legs are the two sides that form the right angle
3
This theorem ONLY works for right triangles
📐 Finding the Hypotenuse
📏 Finding a Missing Leg
Key Takeaways
Identify What's Missing: First, determine if you're looking for the hypotenuse or a leg.
Finding Hypotenuse: Square both legs, ADD them together, then take the square root.
Finding a Leg: Square the hypotenuse and the known leg, SUBTRACT, then take the square root.
Check Your Answer: The hypotenuse must always be longer than either leg!
The Process
Step 1: Identify the hypotenuse (c) and legs (a, b)
Step 2: Set up the equation: a² + b² = c²
Step 3: Substitute known values and solve for the unknown
Step 4: Take the square root to find the missing side
Find the missing side:
Find the length of the hypotenuse (c).
We start with the formula: a² + b² = c²
What is the formula we'll use?
Substitute a = 3 and b = 4 into the formula:
3² + 4² = c²
What is 3²?
Now we have: 9 + 16 = c²
9 + 16 = ?
c² = 25, so we need to find c = √25
c = √25 = ?
🎉
Excellent!
The hypotenuse c =
5
This is the famous 3-4-5 right triangle!
Find the missing side:
Find the length of the missing leg (a).
Start with: a² + b² = c²
We know b = 12 and c = 13, so: a² + 12² = 13²
What is 13² (the hypotenuse squared)?
🎉
Excellent!
The missing leg a =
5
5-12-13 is another Pythagorean triple!
Find the missing side:
Find the length of the hypotenuse (c).
🎉
Excellent!
The hypotenuse c =
10
6-8-10 is a multiple of the 3-4-5 triangle!
Remember!
a² + b² = c²
Finding hypotenuse: c = √(a² + b²)
Finding a leg: a = √(c² - b²)
1. Legs: 5 and 12
Find the hypotenuse (c)
2. Leg: 8, Hypotenuse: 17
Find the missing leg
3. Legs: 9 and 12
Find the hypotenuse (c)
4. Leg: 5, Hypotenuse: 13
Find the missing leg
5. Legs: 7 and 24
Find the hypotenuse (c)
6. Leg: 9, Hypotenuse: 15
Find the missing leg
7. Legs: 8 and 15
Find the hypotenuse (c)
8. Leg: 20, Hypotenuse: 25
Find the missing leg
9. Legs: 9 and 40
Find the hypotenuse (c)
10. Leg: 7, Hypotenuse: 25
Find the missing leg
Great Work!
0/10
Problems Correct
🎉
Congratulations!
You've completed the Pythagorean Theorem lesson!
You can now find missing sides of right triangles.
What You Learned
✓ The Pythagorean Theorem: a² + b² = c²
✓ Finding the hypotenuse:
• c = √(a² + b²)
✓ Finding a missing leg:
• a = √(c² - b²)
✓ Common Pythagorean triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25
Your Final Score
0/13
Total Problems Completed
Finding Missing Sides - Pythagorean Theorem Results
Student Name:
Date:
Florida Standards Covered
MA.8.GR.1.1 - Apply the Pythagorean Theorem to solve mathematical and real-world problems involving unknown side lengths in right triangles.
Guided Practice (3 Problems)
1. Legs: 3, 4 → Hypotenuse
c = 5 ✓
2. Leg: 12, Hypotenuse: 13 → Missing Leg
a = 5 ✓
3. Legs: 6, 8 → Hypotenuse
c = 10 ✓
Independent Practice (10 Problems)