Draw every line of symmetry for the hexagon. For polygons with an even
number of sides, all lines of symmetry pass through either - (pick two)
two vertices one vertex and one side two sides

Question

Draw every line of symmetry for the hexagon. For polygons with an even
number of sides, all lines of symmetry pass through either - (pick two)
two vertices

one vertex and one side two sides

UpStudy AI · Accepted Answer

For a regular hexagon, which has six sides, the lines of symmetry can be categorized based on the options provided.

1. **Two vertices**: A line of symmetry can be drawn connecting two opposite vertices.
2. **One vertex and one side**: A line of symmetry can also be drawn from a vertex to the midpoint of the opposite side.

### Step-by-step Explanation:

1. **Identify the vertices**: Label the vertices of the hexagon as $$ A, B, C, D, E, F $$.
2. **Draw lines through two vertices**: 
   - Lines can be drawn from $$ A $$ to $$ D $$, $$ B $$ to $$ E $$, and $$ C $$ to $$ F $$. These lines will divide the hexagon into two mirror-image halves.
3. **Draw lines from one vertex to one side**:
   - A line can be drawn from vertex $$ A $$ to the midpoint of side $$ BC $$.
   - Similarly, lines can be drawn from $$ B $$ to the midpoint of side $$ CD $$, from $$ C $$ to the midpoint of side $$ DE $$, from $$ D $$ to the midpoint of side $$ EF $$, from $$ E $$ to the midpoint of side $$ FA $$, and from $$ F $$ to the midpoint of side $$ AB $$.

### Summary of Lines of Symmetry:
- **Through two vertices**: $$ AD, BE, CF $$
- **Through one vertex and one side**: $$ A $$ to midpoint of $$ BC $$, $$ B $$ to midpoint of $$ CD $$, $$ C $$ to midpoint of $$ DE $$, $$ D $$ to midpoint of $$ EF $$, $$ E $$ to midpoint of $$ FA $$, $$ F $$ to midpoint of $$ AB $$

In total, a regular hexagon has 6 lines of symmetry.

Now, I will draw the hexagon and its lines of symmetry.
Simplify the expression by following steps:
- step0: Solution:
  $$drawaregularhexagonwithlinesofsym	imes metrythroughverticesandmidpointsofsides$$
- step1: Rewrite the expression:
  $$d^{4}r^{6}a^{5}we^{7}g^{3}ulh^{4}xo^{5}n^{4}wi^{6}t^{5}ls^{6}fym^{3}yuvcpf$$
- step2: Evaluate the power:
  $$d^{4}r^{6}a^{5}we^{7}g^{3}ulh^{4}xo^{5}n^{4}w\left(-1ight)t^{5}ls^{6}fym^{3}yuvcpf$$
- step3: Use the rules for multiplication and division:
  $$-d^{4}r^{6}a^{5}we^{7}g^{3}ulh^{4}xo^{5}n^{4}wt^{5}ls^{6}fym^{3}yuvcpf$$
- step4: Multiply the terms:
  $$-d^{4}r^{6}a^{5}w^{2}e^{7}g^{3}ulh^{4}xo^{5}n^{4}t^{5}ls^{6}fym^{3}yuvcpf$$
- step5: Multiply the terms:
  $$-d^{4}r^{6}a^{5}w^{2}e^{7}g^{3}u^{2}lh^{4}xo^{5}n^{4}t^{5}ls^{6}fym^{3}yvcpf$$
- step6: Multiply the terms:
  $$-d^{4}r^{6}a^{5}w^{2}e^{7}g^{3}u^{2}l^{2}h^{4}xo^{5}n^{4}t^{5}s^{6}fym^{3}yvcpf$$
- step7: Multiply the terms:
  $$-d^{4}r^{6}a^{5}w^{2}e^{7}g^{3}u^{2}l^{2}h^{4}xo^{5}n^{4}t^{5}s^{6}f^{2}ym^{3}yvcp$$
- step8: Multiply the terms:
  $$-d^{4}r^{6}a^{5}w^{2}e^{7}g^{3}u^{2}l^{2}h^{4}xo^{5}n^{4}t^{5}s^{6}f^{2}y^{2}m^{3}vcp$$
- step9: Reorder the terms:
  $$-e^{7}d^{4}r^{6}a^{5}w^{2}g^{3}u^{2}l^{2}h^{4}xo^{5}n^{4}t^{5}s^{6}f^{2}y^{2}m^{3}vcp$$
It seems that I cannot directly draw the hexagon and its lines of symmetry. However, I can describe how you can visualize or draw it yourself:

1. **Draw a regular hexagon**: Start by drawing a hexagon with vertices labeled $$ A, B, C, D, E, F $$ in a clockwise manner.

2. **Draw lines through two vertices**:
   - Draw a line from vertex $$ A $$ to vertex $$ D $$.
   - Draw a line from vertex $$ B $$ to vertex $$ E $$.
   - Draw a line from vertex $$ C $$ to vertex $$ F $$.

3. **Draw lines from one vertex to one side**:
   - Find the midpoint of side $$ BC $$ and draw a line from vertex $$ A $$ to this midpoint.
   - Repeat this for the other vertices:
     - From $$ B $$ to the midpoint of $$ CD $$
     - From $$ C $$ to the midpoint of $$ DE $$
     - From $$ D $$ to the midpoint of $$ EF $$
     - From $$ E $$ to the midpoint of $$ FA $$
     - From $$ F $$ to the midpoint of $$ AB $$

This will give you a total of 6 lines of symmetry for the hexagon. Each line divides the hexagon into two symmetrical halves.
A regular hexagon has 6 lines of symmetry. These lines include: 1. **Through two vertices**: Lines connecting opposite vertices (e.g., from vertex A to vertex D). 2. **Through one vertex and one side**: Lines from each vertex to the midpoint of the opposite side (e.g., from vertex A to the midpoint of side BC). In total, there are 6 lines of symmetry for a regular hexagon.

Draw every line of symmetry for the hexagon. For polygons with an even
number of sides, all lines of symmetry pass through either - (pick two)
two vertices one vertex and one side two sides

Solución de inteligencia artificial de Upstudy

Responder

Solución

Step-by-step Explanation:

Summary of Lines of Symmetry:

Beyond the Answer

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Latest Geometry Questions

Draw every line of symmetry for the hexagon. For polygons with an even number of sides, all lines of symmetry pass through either - (pick two) two vertices one vertex and one side two sides

Solución de inteligencia artificial de Upstudy

Responder

Solución

Step-by-step Explanation:

Summary of Lines of Symmetry:

Beyond the Answer

preguntas relacionadas

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Draw every line of symmetry for the hexagon. For polygons with an even
number of sides, all lines of symmetry pass through either - (pick two)
two vertices one vertex and one side two sides