Lines of Symmetry - Maths with Mum - Free Printable

Problem Description:

The task involves identifying and drawing the lines of symmetry for each given shape and stating how many lines of symmetry exist for each shape. The provided image shows six shapes with their respective lines of symmetry already drawn, along with the number of lines of symmetry indicated.

Solution Explanation:

#### Step 1: Understanding Lines of Symmetry
A line of symmetry is a line that divides a shape into two identical halves such that one half is the mirror image of the other. To determine the lines of symmetry for a shape:
- Draw a line through the shape.
- Check if the shape on one side of the line is a perfect mirror image of the shape on the other side.
- Repeat this process for all possible orientations (horizontal, vertical, diagonal).

#### Step 2: Analyzing Each Shape

##### Shape (a): Rectangle
- Description: A rectangle has opposite sides equal and parallel, and all angles are right angles.
- Lines of Symmetry:
- There are two lines of symmetry: one vertical line passing through the midpoint of the longer sides and one horizontal line passing through the midpoint of the shorter sides.
- Number of Lines of Symmetry: 2

##### Shape (b): Isosceles Trapezoid
- Description: An isosceles trapezoid has one pair of parallel sides (bases) and the non-parallel sides (legs) are equal in length.
- Lines of Symmetry:
- There is one vertical line of symmetry passing through the midpoints of the two parallel sides.
- Number of Lines of Symmetry: 1

##### Shape (c): Equilateral Triangle
- Description: An equilateral triangle has all three sides of equal length and all three angles of 60°.
- Lines of Symmetry:
- There are three lines of symmetry: one from each vertex to the midpoint of the opposite side.
- Number of Lines of Symmetry: 3

##### Shape (d): Regular Pentagon
- Description: A regular pentagon has five equal sides and five equal angles.
- Lines of Symmetry:
- There are five lines of symmetry: one from each vertex to the midpoint of the opposite side.
- Number of Lines of Symmetry: 5

##### Shape (e): Parallelogram
- Description: A parallelogram has opposite sides equal and parallel, but it is not necessarily symmetric unless it is a special type (e.g., rectangle, rhombus, or square).
- Lines of Symmetry:
- A general parallelogram does not have any lines of symmetry unless it is a special case like a rectangle, rhombus, or square.
- Number of Lines of Symmetry: 0

##### Shape (f): Crescent Moon
- Description: This shape resembles a crescent moon, which is asymmetrical except for one specific orientation.
- Lines of Symmetry:
- There is one vertical line of symmetry passing through the center of the shape.
- Number of Lines of Symmetry: 1

#### Step 3: Summarizing the Results
The number of lines of symmetry for each shape is as follows:
- (a) Rectangle: 2
- (b) Isosceles Trapezoid: 1
- (c) Equilateral Triangle: 3
- (d) Regular Pentagon: 5
- (e) Parallelogram: 0
- (f) Crescent Moon: 1

Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{(a)} & 2 \\
\text{(b)} & 1 \\
\text{(c)} & 3 \\
\text{(d)} & 5 \\
\text{(e)} & 0 \\
\text{(f)} & 1 \\
\end{array}
}
\]