Question

determine whether each figure has a line of symmetry. if so, draw the lines of symmetry and state how many lines of symmetry it has. 1. 2. 3. 4. 5. 6.

Explanation:

Figure 1 (Triangle)

Step1: Identify Triangle Type

The triangle appears equilateral (all sides/angles equal).

Step2: Lines of Symmetry

An equilateral triangle has 3 lines of symmetry (each from a vertex to the midpoint of the opposite side).

Figure 2 (Hexagon - Likely a Rhombus - Shaped Hexagon)

Step1: Analyze Shape

It is a symmetric hexagon (like a stretched rectangle with pointed ends).

Step2: Lines of Symmetry

It has 2 lines of symmetry: one vertical (through the center, splitting the pointed ends) and one horizontal (through the center, splitting the top and bottom sides).

Figure 3 (Right - Angled Scalene Triangle)

Step1: Triangle Type

It is a right - angled triangle with all sides of different lengths (scalene).

Step2: Lines of Symmetry

A scalene right - angled triangle has no lines of symmetry (no way to fold it to match both sides).

Figure 4 (Parallelogram)

Step1: Parallelogram Properties

A general parallelogram (non - rhombus, non - rectangle) has no lines of symmetry (folding along any line won’t make both sides match).

Figure 5 (Regular Pentagon)

Step1: Regular Polygon

A regular pentagon has equal sides and angles.

Step2: Lines of Symmetry

A regular pentagon has 5 lines of symmetry (each from a vertex to the midpoint of the opposite side).

Figure 6 (Regular Octagon)

Step1: Regular Polygon

A regular octagon has 8 equal sides and angles.

Step2: Lines of Symmetry

A regular octagon has 8 lines of symmetry (4 through opposite vertices, 4 through midpoints of opposite sides).

Answer:

1. The figure (equilateral triangle) has 3 lines of symmetry.
2. The figure has 2 lines of symmetry.
3. The figure (right - angled scalene triangle) has 0 lines of symmetry.
4. The figure (parallelogram) has 0 lines of symmetry.
5. The figure (regular pentagon) has 5 lines of symmetry.
6. The figure (regular octagon) has 8 lines of symmetry.