Problem

Which figure has an order of reflectional symmetry that is greater than 4 ? Isosceles trapezoid Rectangle Equilateral triangle Regular pentagon

Solution

Step 1 :The order of reflectional symmetry of a figure is the number of times the figure can be reflected over a line and still look the same.

Step 2 :An isosceles trapezoid has an order of reflectional symmetry of 1, because it can only be reflected over a vertical line through the middle of the figure.

Step 3 :A rectangle has an order of reflectional symmetry of 2, because it can be reflected over a vertical line through the middle of the figure and a horizontal line through the middle of the figure.

Step 4 :An equilateral triangle has an order of reflectional symmetry of 3, because it can be reflected over three different lines, each passing through a vertex and the midpoint of the opposite side.

Step 5 :A regular pentagon has an order of reflectional symmetry of 5, because it can be reflected over five different lines, each passing through a vertex and the midpoint of the opposite side.

Step 6 :So, the figure with an order of reflectional symmetry greater than 4 is the regular pentagon.

Step 7 :Final Answer: \(\boxed{\text{Regular pentagon}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/ENGn0wyATi/

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