To solve this maze, we need to use the Converse of the Pythagorean Theorem. This theorem helps us figure out if a triangle is right, acute, or obtuse based on its side lengths.
Here’s how it works:
- If $a^2 + b^2 = c^2$, the triangle is a
right triangle.
- If $a^2 + b^2 > c^2$, the triangle is an
acute triangle.
- If $a^2 + b^2 < c^2$, the triangle is an
obtuse triangle.
In each case, $c$ is the longest side.
Let’s go step by step through the maze:
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Step 1: Start at 9, 12, 15
Check: $9^2 + 12^2 = 81 + 144 = 225$
$15^2 = 225$
Since $225 = 225$, it’s a
right triangle.
→ Follow the “Right” path → leads to 4, 6, 7
---
Step 2: 4, 6, 7
Longest side is 7.
Check: $4^2 + 6^2 = 16 + 36 = 52$
$7^2 = 49$
Since $52 > 49$, it’s an
acute triangle.
→ Follow the “Acute” path → leads to 9, 4, 12
---
Step 3: 9, 4, 12
Longest side is 12.
Check: $9^2 + 4^2 = 81 + 16 = 97$
$12^2 = 144$
Since $97 < 144$, it’s an
obtuse triangle.
→ Follow the “Obtuse” path → leads to √11, 5, 6
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Step 4: √11, 5, 6
Longest side is 6.
Check: $(\sqrt{11})^2 + 5^2 = 11 + 25 = 36$
$6^2 = 36$
Since $36 = 36$, it’s a
right triangle.
→ Follow the “Right” path → leads to 6, 12, 13
---
Step 5: 6, 12, 13
Longest side is 13.
Check: $6^2 + 12^2 = 36 + 144 = 180$
$13^2 = 169$
Since $180 > 169$, it’s an
acute triangle.
→ Follow the “Acute” path → leads to 1, 3, √10
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Step 6: 1, 3, √10
Longest side is √10 ≈ 3.16
Check: $1^2 + 3^2 = 1 + 9 = 10$
$(\sqrt{10})^2 = 10$
Since $10 = 10$, it’s a
right triangle.
→ Follow the “Right” path → leads to Finish!!
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✔ We’ve reached the finish! The correct path is:
Start → Right → Acute → Obtuse → Right → Acute → Right → Finish
Final Answer:
The correct path through the maze is: Start → Right → Acute → Obtuse → Right → Acute → Right → Finish!!
Parent Tip: Review the logic above to help your child master the concept of converse of the pythagorean theorem worksheet.
