Group by Convexity
Group by Convexity problems involve classifying figures based on whether they are convex (all interior angles < 180°, shape bulges outward) or concave (has at least one interior angle > 180°, has an indentation or 'caved-in' region). These problems test understanding of geometric convexity and shape boundary analysis.
What You'll Learn
Introduction to Group by Convexity
Group by Convexity problems involve classifying figures based on whether they are convex (all interior angles < 180°, shape bulges outward) or concave (has at least one interior angle > 180°, has an indentation or 'caved-in' region). These problems test understanding of geometric convexity and shape boundary analysis.
Prerequisites
How to Solve Group by Convexity Problems
Step 1: Examine each figure for indentations or 'caved-in' regions
Step 2: Convex shapes: all interior angles < 180°, shape bulges outward
Step 3: Concave shapes: has at least one interior angle > 180°, has indentation
Step 4: Group convex shapes together
Step 5: Group concave shapes together
Step 6: The classification basis is convexity
Example Problem
Example: Three convex shapes (circle, square, triangle), three concave shapes (star, arrow, cross). How are they grouped? Solution: Step 1: Convex shapes: all interior angles <180°, no indentations Step 2: Concave shapes: have indentations or interior angles >180° Step 3: Group 1: Convex shapes Step 4: Group 2: Concave shapes Step 5: Classification basis = Convexity Answer: Grouped by convexity - convex shapes vs concave shapes
Pro Tips & Tricks
- Convex shapes: circle, square, triangle, pentagon, hexagon
- Concave shapes: star, arrow, cross, crescent, heart
- All regular polygons are convex
- Stars are concave (they have indentations between points)
- Arrows are concave (the notch creates an indentation)
- The letter 'C' is concave, 'O' is convex
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Group by Convexity. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Group by Convexity is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Group by Convexity?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: