Converse of Pythagorean Theorem Worksheet/Game

Converse of Pythagorean Theorem Worksheet/Game
Welcome to Converse of Pythagorean Theorem Worksheet/Game. This game focuses on how to use the Converse of Pythagorean Theorem to classify a triangle. Your goal is to determine if a triangle is Acute, Right, or Obtuse based on its side lengths.

 

 

1. The Inspection Logic
   To play, you must compare the squares of the sides. Always identify the longest side first and call it c. The two shorter sides are a and b.
   Right Triangle: If a² + b² = c².
   Acute Triangle: If a² + b² > c².
   Obtuse Triangle: If a² + b² < c².
   

2. How to Play
   Analyze the Profile: Look at the three numbers provided in the Dimension Profile box.
   Run the Calculation:
   Square the two smaller numbers and add them together.
   Square the largest number.
   Compare the two results.
   Select the Type: Click the button (Acute, Right, or Obtuse) that matches your result.
   Verify & Advance: If you are correct, the button turns yellow (“Correct”). If wrong, it turns red.
   Click Next Inspection to move to the next problem.
   

3. Memorize Triples:
   If you see 3, 4, 5 or 5, 12, 13, you don’t even need to calculate—those are always Right triangles.
   Check the Squares:
   Example: For sides 3, 3, 5:
   3² + 3² = 9 + 9 = 185² = 25
   Since 18 < 25, it is Obtuse.
   

If…	Then the Triangle is…	Visual Intuition
a2 + b2 = c2	Right	The sides fit perfectly to form a 90° angle.
a2 + b2 > c2	Acute	The “hypotenuse” is too short, pushing the angles inward.
a2 + b2 < c2	Obtuse	The “hypotenuse” is very long, stretching one angle past 90°

Converse of Pythagorean Theorem

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