Problem Analysis:
The task involves identifying and analyzing symmetry in geometric shapes. Symmetry is a property where one half of an object is a mirror image of the other half when divided by a line (line of symmetry).
#### Part 1: Circle the image which has a line of symmetry
We need to identify which of the three given images has at least one line of symmetry.
1.
Equilateral Triangle:
- An equilateral triangle has
3 lines of symmetry (each passing through a vertex and the midpoint of the opposite side).
- It is symmetric along these lines.
2.
Heart Shape:
- The heart shape has
1 line of symmetry (vertical line passing through the center).
- It is symmetric along this vertical line.
3.
Checkmark Symbol:
- The checkmark symbol does not have any line of symmetry.
- There is no way to divide it into two identical halves.
Conclusion for Part 1:
The images with a line of symmetry are the
equilateral triangle and the
heart shape. However, since only one needs to be circled, we can choose either. For clarity, let's circle the
heart shape as it is more straightforward.
---
#### Part 2: Find and draw all lines of symmetry for the following figures
We need to analyze each figure, determine its lines of symmetry, and write the number of lines of symmetry below each figure.
1.
Figure 1: Arrowhead (Double-Arrow)
- This shape has
1 line of symmetry (vertical line passing through the center).
- Drawing the line shows that the left and right sides are mirror images.
2.
Figure 2: Right Triangle
- This is a
scalene triangle (no equal sides or angles).
- It has
0 lines of symmetry because no line can divide it into two identical halves.
3.
Figure 3: Triangular Shape with a Base
- This shape resembles an
isosceles triangle with a flat base.
- It has
1 line of symmetry (vertical line passing through the apex and the midpoint of the base).
4.
Figure 4: Trapezoid
- This is an
isosceles trapezoid (non-parallel sides are equal).
- It has
1 line of symmetry (vertical line passing through the midpoints of the parallel sides).
5.
Figure 5: Square
- A square has
4 lines of symmetry:
- 2 vertical/horizontal lines passing through the center.
- 2 diagonal lines.
- Drawing these lines confirms the symmetry.
6.
Figure 6: Pentagon
- This is a
regular pentagon (all sides and angles are equal).
- It has
5 lines of symmetry:
- Each line passes through a vertex and the midpoint of the opposite side.
---
Final Answers:
#### Part 1:
Circle the
heart shape.
#### Part 2:
- Figure 1: Arrowhead →
1 line of symmetry
- Figure 2: Right Triangle →
0 lines of symmetry
- Figure 3: Triangular Shape with a Base →
1 line of symmetry
- Figure 4: Trapezoid →
1 line of symmetry
- Figure 5: Square →
4 lines of symmetry
- Figure 6: Pentagon →
5 lines of symmetry
Boxed Final Answer:
\[
\boxed{
\begin{array}{c}
\text{Part 1: Heart Shape} \\
\text{Part 2: } 1, 0, 1, 1, 4, 5
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of line of symmetry worksheet.
