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Triangles Star

Star Figure Triangle Counting problems involve counting triangles in 5-pointed stars (pentagrams) and 6-pointed stars (hexagrams). These figures contain many intersecting lines that create numerous triangles of various sizes and orientations.

10Worksheets
200+Practice Questions
HardDifficulty
2-3 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Triangles Star

Star Figure Triangle Counting problems involve counting triangles in 5-pointed stars (pentagrams) and 6-pointed stars (hexagrams). These figures contain many intersecting lines that create numerous triangles of various sizes and orientations.

Prerequisites

Understanding of star geometry Ability to identify overlapping triangles Systematic counting methods Pattern recognition skills
Why This Matters: Star Figure problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test advanced visual pattern recognition.

How to Solve Triangles Star Problems

1

Step 1: Identify the type of star figure (5-pointed or 6-pointed)

2

Step 2: For 5-pointed star: Count small triangles at each point (5 triangles)

3

Step 3: Count larger triangles formed by intersecting lines (5 triangles)

4

Step 4: Total for 5-pointed star = 10 triangles

5

Step 5: For 6-pointed star (Star of David): Count small triangles at points (6 small)

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Step 6: Count the two large overlapping triangles (2 large)

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Step 7: Total for 6-pointed star = 8 triangles

Pro Strategy: For star figures, identify the basic geometric shape first. In a pentagram, there are small isosceles triangles at each point and larger triangles formed by the intersecting lines. Use color-coding or labeling to track counted triangles.

Example Problem

Example: Count the number of triangles in a 5-pointed star (pentagram). Solution: Step 1: The figure is a 5-pointed star (like the one on the US flag) Step 2: Small triangles at the 5 points: 5 triangles Step 3: Larger triangles formed by connecting alternate points: 5 triangles Step 4: Total triangles = 5 + 5 = 10 Answer: 10 triangles

Pro Tips & Tricks

  • 5-pointed star (pentagram): 10 triangles total (5 small point triangles + 5 larger triangles)
  • 6-pointed star (Star of David/hexagram): 8 triangles total (6 small point triangles + 2 large overlapping triangles)
  • The Star of David is formed by two overlapping equilateral triangles
  • In a pentagram, the intersection points create a smaller pentagon inside
  • Some advanced star figures may have additional triangles (up to 35 in some configurations)
  • Always label intersection points to avoid missing triangles

Shortcut Methods to Solve Faster

Pentagram always has 10 triangles
Hexagram (Star of David) always has 8 triangles
In some complex star figures, there may be 30 or more triangles
For a regular pentagram, the number of triangles is fixed at 10

Common Mistakes to Avoid

Counting only the point triangles and missing the larger ones
Counting the central pentagon as a triangle (it's not a triangle)
In a hexagram, forgetting that the two large triangles are also triangles
Double-counting triangles that share the same vertices

Exam Importance

Triangles Star is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
1-2 questions
CAT
1-2 questions
INSURANCE
1-2 questions

Ready to Master Triangles Star?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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