Question

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2.b. how many lines of symmetry does the figure have? how do you know whether you have found them all?

Explanation:

Step1: Recall the definition of a line of symmetry

A line of symmetry is a line that divides a figure into two congruent (identical) parts.

Step2: Analyze the isosceles trapezoid

For an isosceles trapezoid (the given figure), the only line of symmetry is the vertical line that passes through the mid - points of the two parallel sides.

Step3: Check for other possible lines of symmetry

• Horizontal line: If we draw a horizontal line through the trapezoid, the upper and lower parts are not congruent.
• Diagonal lines: If we draw diagonal lines, the two parts formed are not congruent.

Answer:

The figure (an isosceles trapezoid) has \(1\) line of symmetry. We know we have found them all by checking all possible orientations (horizontal, vertical, diagonal) of lines that could potentially divide the figure into congruent parts. Only the vertical line through the mid - points of the parallel sides works.