Wei Lin's art teacher shows her four geometric figures and asks her to identify which one is NOT a line-symmetric figure. Figure A: A regular hexagon (all 6 sides equal, all 6 interior angles equal) Figure B: An isosceles triangle (two sides equal, one line of symmetry) Figure C: A parallelogram (opposite sides parallel and equal, but NO right angles) Figure D: A rectangle (all angles 90°, opposite sides equal) Which figure is NOT line-symmetric?
Show Worked Solution
Worked Solution
Step 1: Test Figure A — Regular hexagon.
A regular hexagon has 6 equal sides and 6 equal angles. It has 6 lines of symmetry (3 through opposite vertices, 3 through midpoints of opposite sides). It IS line-symmetric.
Step 2: Test Figure B — Isosceles triangle.
An isosceles triangle has 2 equal sides. The perpendicular bisector of the base is a line of symmetry — folding along it maps the two equal sides onto each other perfectly. It IS line-symmetric (1 line of symmetry).
Step 3: Test Figure C — Parallelogram (NOT a rectangle or rhombus).
A parallelogram has opposite sides parallel and equal, but no right angles and no equal adjacent sides. Try any line through the parallelogram: a vertical line through the midpoints cuts across unequal lengths on each half; a horizontal line does the same; the diagonals are not lines of symmetry either. A parallelogram has 0 lines of symmetry. It is NOT line-symmetric. (Note: it does have 180° rotational symmetry, but that is NOT the same as line symmetry.)
Step 4: Test Figure D — Rectangle.
A rectangle has 2 lines of symmetry — the horizontal and vertical midlines. Folding along either midline maps one half exactly onto the other. It IS line-symmetric.
Answer: Figure C (Parallelogram) — it has 0 lines of symmetry.
Correct answer: Figure C (Parallelogram)
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