Why is the answer 1 line of symmetry?
First, understand the object:
- A divider has two identical metal legs joined at the top.
- When you open it equally, both legs make the same angle on each side.
What is a line of symmetry?
- A line of symmetry is a line that splits a shape into two mirror halves.
- If you fold the shape along this line, the two halves match exactly.
Apply this to the divider:
- Imagine the two legs form an angle at the joint. Call the joint point O.
- Let the tips of the legs touch the paper at points A and B.
- The angle between the legs is ( angle AOB ).
- The angle bisector is the line that cuts this angle into two equal parts.
- Draw a line from the joint O straight between the two legs. This is the bisector.
Why is that line the only symmetry line?
- On this line (the bisector), each point on the left leg has a matching point on the right leg, the same distance from the line.
- This means the two legs are mirror images across this line.
In math terms (small steps):
The bisector makes the two small angles equal:
( angle AOX ) is equal to ( angle XOB ).
So, ( angle AOX = angle XOB ).
Here, ( OX ) is the bisector (the symmetry line).
Important note:
- This works only when the divider is opened equally (both legs at the same angle).
- If one leg is opened more than the other (unequal), then there is no line of symmetry.
Conclusion: A divider with identical legs opened equally has one line of symmetry — the line along the angle bisector passing through the joint.