Completing an Incomplete Figure

🎯 Learning Objective

Choose the piece that completes a figure by continuing its symmetry or repeating pattern.

💡 Concept

• A part of a symmetric figure is missing — pick the option that restores the pattern
• First find the symmetry: a mirror line (reflection) or a centre of rotation
• Mirror symmetry: the missing part is the exact reflection of the visible part across the axis
• Rotational symmetry: rotate the visible part by the fixed step (90°, 120°…) to get the missing part
• Every line, curve and shaded area must continue smoothly where the pieces meet
• Match the boundary: lines touching the join must line up exactly with the given figure

✏️ Easy Example

Q. A design is symmetric about a vertical centre line. Its left half has a black dot in the top-left corner. Where must the matching black dot appear on the right half?

1. A vertical mirror line swaps left and right, keeps top and bottom
2. The top-left corner reflects to the top-right corner

Answer: In the top-right corner of the right half

🇮🇳 Real-Life Example

Drawing a rangoli, you complete the missing quarter by mirroring the part you already drew — the exam's figure-completion is that same instinct.

📝 Exam-Level Example

Q. A square tile is split into four quadrants. Three quadrants each show an arrow, and each arrow is the previous one turned 90° clockwise. What should the empty fourth quadrant show?

1. The pattern is a fixed 90° clockwise rotation step
2. Continue it: the fourth arrow is the third one turned 90° clockwise

Answer: An arrow rotated 90° clockwise from the third quadrant's arrow

📝 Exam-Level Example

Q. The upper half of a figure symmetric about a horizontal line shows a small triangle pointing UP on the left. What must the lower half show at the same spot?

1. A horizontal mirror line swaps top and bottom, keeps left and right
2. An up-pointing triangle reflects to a down-pointing triangle, staying on the left

Answer: A downward-pointing triangle on the left of the lower half

🪄 Memory Trick

Find the axis or centre of symmetry first; the answer is just the visible part copied across it — reflected for a mirror line, rotated for a centre.

⚠️ Common Mistakes

• ❌ Rotating the piece when the figure actually needs a mirror reflection (or the reverse)
• ❌ Ignoring shading — the completed part must match black and white areas too
• ❌ Not checking that lines meet exactly at the join with the given figure

🏆 Exam Tips

• ✅ Mentally fold the figure along the axis — the two halves must match perfectly
• ✅ Check the corners and edges where the missing piece meets the rest

📌 Summary

• Restore the figure's symmetry or repeating pattern
• Mirror line → reflect the visible part; centre → rotate it
• Match lines, curves AND shading at the join
• Fold-check along the axis to confirm