Question

1. for each of the following figures, draw all lines of reflection that could be used to map the figure onto itself. verify using tracing paper. there is one figure that has no lines of symmetry.

Explanation:

Step1: Recall line - symmetry concept

A line of symmetry is a line that divides a figure into two congruent parts such that the figure on one side of the line is the mirror image of the figure on the other side.

Step2: Analyze rectangle (a)

A rectangle has 2 lines of symmetry, one horizontal and one vertical.

Step3: Analyze square (b)

A square has 4 lines of symmetry, two diagonals, one horizontal and one vertical.

Step4: Analyze parallelogram (c)

A parallelogram has no lines of symmetry. Folding it along any line will not result in the two halves being mirror - images of each other.

Step5: Analyze regular hexagon (d)

A regular hexagon has 6 lines of symmetry.

Step6: Analyze isosceles trapezoid (e)

An isosceles trapezoid has 1 line of symmetry.

Step7: Analyze right - angled triangle (f)

A non - isosceles right - angled triangle has no lines of symmetry. An isosceles right - angled triangle has 1 line of symmetry. Assuming a non - isosceles case here, it has no lines of symmetry. But the parallelogram (c) is the most well - known non - symmetric quadrilateral among these common shapes.

Answer:

The figure that has no lines of symmetry is (c) the parallelogram.