Completion of Figure

 In Completion of Figure, you are given an incomplete figure, and you have to identify the missing part from the options to complete the original design or pattern correctly.

It tests your visual perception, symmetry sense, and spatial reasoning.

Key Skills Required:

• Pattern recognition

• Visual symmetry understanding

• Logical sequencing

📘 Types of Problems

Type	Description	Example
Pattern Completion	Find the missing part of a repeating pattern	Complete the sequence: △ ◯ □ △ ◯ ?
Symmetry Completion	Finish the mirror image or rotational symmetry	Complete the half-drawn symmetrical shape
Figure Series Completion	Identify the next figure in a logical sequence	Predict the next shape in: →, ↗, ↑, ...
Partial Figure Completion	Select the piece that fits into an incomplete figure	Choose the fragment that completes a puzzle

🧠 Core Solving Methods

Method 1: Pattern Analysis

1. Identify the repeating sequence

2. Determine the missing element

Example:
Complete: ◰, ◳, ◱, ◲, ?
Solution: The pattern rotates 90° clockwise each step → Next is ◰.

Method 2: Symmetry Completion

1. Draw the axis of symmetry

2. Mirror the existing half

Example:
Complete the symmetrical figure:

  /\
 /  ?

Answer: Mirror image → \ to form a diamond (◇).

Method 3: Logical Progression

1. Analyze changes between consecutive figures

2. Apply the same transformation

Example:
Series: □, ◇, ○, ... (shrinking sides)
Next shape: • (dot)

🎯Important Concepts with Diagrams

Concept 1: Linear Patterns

Pattern: ■, ■■, ■■■, ?  
Next: ■■■■ (adds one ■ each time)

Concept 2: Rotational Patterns

Sequence: |, /, —, \  
Next: | (completes 90° rotation cycle)

Concept 3: Geometric Transformation

Series: ▲, ◭, ◢, ?  
Solution: ◣ (shrinking right side each step)

🧩 Practice Questions with Diagrams

Q1: Pattern Completion

Complete: ♠, ♣, ♥, ?
Options: A: ♦ B: ♠ C: ♫
Answer: A: ♦ (completes card suits sequence)

Q2: Symmetry Completion

Given half: /|  
Missing part: ?

Answer: |\ (forms a ▲)

Q3: Figure Series

Series: □, ◇, ○, •, ?
Answer: ∅ (shrinking to nothing)

Q4: Partial Completion

Incomplete: [∿  
Missing piece: ?
Options: A: ⏋ B: ∿ C: ⏌]

Answer: C: ⏌] (completes the square bracket)

Q5: Rotational Symmetry

Partial: ⬏  
Complete with: ?
Options: A: ⬎ B: ⬑ C: ⬒

Answer: B: ⬑ (forms 90° rotational symmetry)

💡 Advanced Techniques

1. Grid Method: Divide complex figures into grids to spot patterns

2. Colour Coding: Use colours to track repeating elements

3. Overlay Technique: Mentally overlay options to check fits

Example of Grid Method:

Incomplete: 
■ □ ■
□ ■ ?

Solution: Checkerboard pattern → Next is □

📝 Common Mistakes to Avoid

• Ignoring small details in complex patterns

• Assuming only one type of symmetry (mirror vs rotational)

• Overlooking alternating colour patterns

📘 Practice Questions – Completion of Figure

Q1: Pattern Completion

Problem: Complete the sequence:

▲, ◀, ▼, ▶, ?  

Options:
A) ▲
B) ◀
C) ◆

Answer: A) ▲
Explanation: The sequence shows 90° clockwise rotation → next shape returns to original position.

Q2: Symmetry Completion

Problem: Complete the symmetrical figure:

  /\
 /  ?

Options:
A) \
B) /
C) |

Answer: A) \
Explanation: Mirror the left half to form a diamond (◇).

Q3: Figure Series

Problem: What comes next?

□, ◇, ○, •, ?  

Options:
A) ∅
B) ■
C) ◌

Answer: A) ∅
Explanation: Shapes progressively shrink to a dot → then disappear.

Q4: Partial Figure Completion

Problem: Select the missing piece:

┌─────┐
│     │
│  ?  │
└─────┘  

Options:
A) ★
B) ◯
C) ■

Answer: C) ■
Explanation: The simplest continuation maintains the rectangular structure.

Q5: Rotational Symmetry

Problem: Complete the pattern:

⬏ + ? = Full Rotation  

Options:
A) ⬑
B) ⬎
C) ⬒

Answer: A) ⬑
Explanation: Combines to form 90° rotational symmetry.

Q6: Grid Pattern Completion

Problem: Fill the missing grid cell:

■ □ ■  
□ ■ ?  

Options:
A) ■
B) □
C) ◆

Answer: B) □
Explanation: Checkerboard pattern alternates ■ and □.

Q7: Line Symmetry

Problem: Complete the mirror image:

/|?  

Options:
A) |\
B) /|
C) |/

Answer: A) |\
Explanation: Forms a symmetrical triangle (▲).

Q8: Progressive Complexity

Problem: Next in series:

◯, ⬠, ⬡, ?  

Options:
A) ⬢
B) ◈
C) ⭔

Answer: A) ⬢
Explanation: Sides increase by 1 each step (circle→pentagon→hexagon→heptagon).

Q9: Embedded Completion

Problem: Which fragment completes the puzzle?

⌈  ?  
⌊___⌋  

Options:
A) _
B) ⎺
C) ⎻

Answer: B) ⎺
Explanation: Matches the horizontal line to complete the square bracket.

Q10: 3D Figure Completion

Problem: Complete the cube net:

  ◻  
◻◻◻  
  ?  

Options:
A) ◻
B) ◼
C) ◻◻

Answer: A) ◻
Explanation: Standard cube net requires 6 faces → one missing square at bottom.