No Reflection

Geometry Level 3

I'm a unique quadrilateral. There are infinite ways to divide me into 2 congruent halves, but none of those halves are mirror images of each other.

What quadrilateral am I?

Rectangle Parallelogram Square Trapezoid Rhombus Kite

Worranat Pakornrat by Worranat Pakornrat , 36, Thailand

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1 solution

By the terms "mirror images", the question implies the line of symmetry, which divides the polygon in halves, and those halves reflect each other with that line in the middle.

Apart from irregular quadrilateral, there are 2 types of quadrilaterals that do not have any line of symmetry: parallelogram and non-isosceles trapezoids. However, only the parallelogram can be divided into numerous congruent figures by drawing a line through the diagonal intersection as shown:

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But when we divide it diagonally then both are mirror images of each other

Sahil Patel - 5 years, 6 months ago

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They aren't. Try folding it with a diagonal as the midline; they never fully cover each other. Only a rhombus, which is a special kind of a parallelogram, has 2 lines of symmetry along their diagonals.

Worranat Pakornrat - 5 years, 6 months ago

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