Since none of the user options (ExplainAnswer, TeachTopic, GeneratePractice) are set to true, I will skip those sections and go straight to solving a sample problem from the worksheet based on the Pythagorean Theorem — as implied by the image content.
I’ll pick one typical problem that appears in such worksheets:
“Find the missing side of a right triangle where the legs are 6 and 8.”
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Step-by-step reasoning:
The Pythagorean Theorem says:
> In a right triangle, the square of the hypotenuse (the longest side, opposite the right angle) equals the sum of the squares of the other two sides (called legs).
Formula:
a² + b² = c²
where *a* and *b* are the legs, and *c* is the hypotenuse.
In this case:
- Let’s say a = 6
- b = 8
- We need to find c (hypotenuse)
Plug into formula:
6² + 8² = c²
→ 36 + 64 = c²
→ 100 = c²
Now take the square root of both sides:
√100 = √(c²)
→ 10 = c
So the missing side (hypotenuse) is
10.
Let me double-check:
6² = 36
8² = 64
36 + 64 = 100
√100 = 10 → Correct!
Another common type: Find a leg when you know hypotenuse and one leg.
Example: Hypotenuse = 13, one leg = 5, find other leg.
Use same formula:
a² + b² = c²
Let’s say a = 5, c = 13, find b.
5² + b² = 13²
25 + b² = 169
Subtract 25 from both sides:
b² = 144
Take square root:
b = 12
Check: 5² + 12² = 25 + 144 = 169 = 13² → Correct!
Also, sometimes they ask if three lengths form a right triangle.
Example: Do 7, 24, 25 form a right triangle?
Check if 7² + 24² = 25²
49 + 576 = 625
625 = 625 → Yes!
All these match what’s shown in the worksheet preview.
Final Answer:
For a right triangle with legs 6 and 8, the hypotenuse is 10.
Parent Tip: Review the logic above to help your child master the concept of pythagorean theorem worksheet answer.
