Non-Verbal Reasoning by Dr. R S Aggarwal-Analytical Reasoning- Short Trick to Finding no of triangle.
Non-Verbal Reasoning by Dr. R S Aggarwal-Analytical Reasoning- Short Trick to Finding no of triangle.
Here’s a short and effective trick to find the number of triangles in Non-Verbal Reasoning problems — especially from books like “Non-Verbal Reasoning” by Dr. R.S. Aggarwal (Analytical Reasoning section).
Contents
🔺 Short Trick to Count Number of Triangles
✅ 1. Use the Triangle Counting Formula (Straight Line Division)
For a triangle divided by lines from one vertex:
No. of triangles = n(n + 1)/2
Where n is the number of divisions inside the triangle.
Example:
If a triangle is divided into 4 parts from one vertex:
= 4(4 + 1)/2 = 10 triangles
✅ 2. Use Layer-Based Count (for Grid/Stacked Triangles)
In stacked or step-triangle figures:
Total triangles = 1 + 3 + 5 + … (odd numbers for each layer)
or
Use formula: n² (where n = number of rows)
Example:
If there are 4 layers (rows of triangles):
Total = 4² = 16 triangles
✅ 3. For Complex Figures – Use Zone Method
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Break the figure into zones or blocks
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Count triangles in each zone separately
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Add all, including big triangles formed by combinations
Tip:
Mark each triangle while counting to avoid duplication.
✅ 4. For Overlapping Squares or Figures
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Check how many smaller triangles are formed inside each square
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Count the overlapping/intersecting ones
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Count bigger triangles formed by combination of smaller ones
🧠 Smart Tip: Use Colors or Labels While Practicing
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Use alphabets like A, B, C… to label corners
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Count small triangles first, then medium, then big
📝 Example from Dr. R.S. Aggarwal (Common Type)
A triangle is divided into 3 parts by drawing 2 lines from the top vertex to the base.
✔ Count each triangle (3 small + 2 medium overlapping + 1 big) = 6 triangles
📚 Practice Examples to Try:
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A star shape (intersecting triangles)
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Pyramid of triangles
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A triangle inside a square
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A figure formed by intersecting diagonals
Would you like:
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✅ A PDF sheet with 25 triangle-counting practice problems?
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✅ Video explanation of the top 5 triangle puzzles?
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✅ A printable formula chart for non-verbal reasoning?
Let me know and I’ll generate it for you.
