Understanding Line of Symmetry

A line of symmetry is a line that divides a figure into two identical halves that mirror each other. If you fold the figure along this line, the two halves match up perfectly.

Line of Symmetry in a Rectangle

Let's look at a rectangle (Figure I). A rectangle has two pairs of equal sides and four right angles. Does it have a line of symmetry? Yes, it does.

• A rectangle has a vertical line of symmetry passing through the midpoints of the longer sides.
• It also has a horizontal line of symmetry passing through the midpoints of the shorter sides.

Folding a rectangle along either of these lines will result in one half perfectly overlapping the other half. Therefore, a rectangle has lines of symmetry.

Line of Symmetry in an Isosceles Triangle

Now consider an isosceles triangle (Figure II). An isosceles triangle is a triangle that has at least two sides of equal length. Does an isosceles triangle have a line of symmetry? Yes, it does.

• An isosceles triangle has one line of symmetry.
• This line of symmetry passes from the vertex between the two equal sides and goes to the midpoint of the opposite side (the base).

Folding an isosceles triangle along this line will make the two equal sides and the two parts of the base coincide perfectly. Thus, an isosceles triangle has a line of symmetry.

Conclusion

Based on our analysis:

• Figure I (Rectangle) has lines of symmetry.
• Figure II (Isosceles triangle) has a line of symmetry.

Therefore, both geometric figures, the rectangle and the isosceles triangle, have lines of symmetry.

Checking the given options, we see that the statement "Both I and II" correctly identifies that both figures have lines of symmetry.