Learn about symmetry through these example problems with detailed step-by-step solutions.
Example 1: Identifying Line Symmetry in a Shape
Does an equilateral triangle have line symmetry? If yes, how many lines of symmetry does it have?
Step 1: A shape has line symmetry if it can be folded along a line so that one half matches the other half perfectly.
Step 2: An equilateral triangle has three equal sides and three equal angles.
Step 3: Check for lines of symmetry by considering folds through each vertex to the midpoint of the opposite side (medians).
Step 4: Each median divides the triangle into two mirror-image halves, and there are three such lines (one through each vertex).
Step 5: Therefore, an equilateral triangle has line symmetry with three lines of symmetry.
Example 2: Checking Line Symmetry in a Letter
Does the letter 'A' have line symmetry? If yes, how many lines of symmetry?
Step 1: Visualize the capital letter 'A' in a standard font (with a horizontal bar, like a triangle with a crossbar).
Step 2: Check for a vertical line of symmetry by folding along the middle of the letter from top to bottom.
Step 3: The left side of 'A' mirrors the right side along this vertical line, so it has vertical symmetry.
Step 4: Check for a horizontal line of symmetry by folding through the middle of the crossbar. The top and bottom do not match.
Step 5: No other lines (e.g., diagonal) produce symmetry.
Step 6: Therefore, the letter 'A' has one line of symmetry (vertical).
Example 3: Determining Symmetry in a Rectangle
How many lines of symmetry does a rectangle (not a square) have?
Step 1: A rectangle has two pairs of equal sides, with opposite sides equal and parallel.
Step 2: Check for a vertical line of symmetry by folding through the middle, parallel to the shorter sides. The left and right halves match.
Step 3: Check for a horizontal line of symmetry by folding through the middle, parallel to the longer sides. The top and bottom halves match.
Step 4: Check for diagonal lines of symmetry. Folding along a diagonal does not produce matching halves (unlike a square).
Step 5: Therefore, a rectangle has two lines of symmetry (one vertical, one horizontal).
Practice Mode
Enter your own problem related to symmetry, and get a step-by-step solution.
Note: This basic solver can currently handle identifying the number of lines of symmetry for common shapes (e.g., equilateral triangle, rectangle, square, circle, letter A, letter B) or letters (e.g., Does the letter A have symmetry?). Enter the shape or letter name clearly.
Related Concepts
Explore these related mathematical concepts to deepen your understanding of symmetry.
Line Symmetry
A shape has line symmetry if it can be folded along a line so that both halves match perfectly.
Lines of Symmetry
The number of lines along which a shape can be folded to produce mirror images varies by shape.
Regular Polygons
Regular polygons (e.g., equilateral triangle, square) have lines of symmetry equal to their number of sides.
Symmetry in Letters
Some letters of the alphabet exhibit line symmetry, depending on their shape in a standard font.
