Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
A figure has line symmetry if a line can be drawn dividing the figure into two identical parts such that when folded along that line, the two parts coincide exactly.
The line that divides a figure into two identical halves is called the 'Line of Symmetry' or the 'Axis of Symmetry'.
A figure may have no line of symmetry, one line of symmetry, or multiple lines of symmetry.
Regular polygons (polygons with all sides and angles equal) are symmetrical. The number of lines of symmetry in a regular polygon is equal to the number of its sides .
In reflection symmetry, the object and its image are at the same distance from the mirror line (line of symmetry). The line of symmetry acts as the perpendicular bisector of the segment joining the object point and its image point.
A scalene triangle has lines of symmetry, an isosceles triangle has line of symmetry, and an equilateral triangle has lines of symmetry.
📐Formulae
💡Examples
Problem 1:
How many lines of symmetry does a regular pentagon have?
Solution:
Explanation:
A regular pentagon is a regular polygon with sides. According to the property of regular polygons, the number of lines of symmetry is equal to the number of sides, which is .
Problem 2:
Identify the number of lines of symmetry in a rectangle that is not a square.
Solution:
Explanation:
A rectangle has two lines of symmetry: one passing through the midpoints of the opposite horizontal sides and one passing through the midpoints of the opposite vertical sides. The diagonals are not lines of symmetry for a rectangle unless it is a square.
Problem 3:
An object point is placed at a distance of from a mirror line . At what distance from the mirror line will its image be formed?
Solution:
Explanation:
In reflection symmetry, the distance of the image from the mirror line is equal to the distance of the object from the mirror line. Therefore, distance = .