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Lines of symmetry of a scalene triangle

Step by step, with the reason for every step · Symmetry · Geometry

Step by step

The question

Question: how many lines of symmetry does a scalene triangle have?

1 Try the folds

Imagine folding the shape along a line.

If the two halves match exactly, it is a line of symmetry.

Fold straight down the middle.

The corners do not meet.

It is not a line of symmetry.

Fold through a corner and the middle of the opposite side.

The corners do not meet.

It is not a line of symmetry.

2 Count the lines

No fold works.

So a scalene triangle has 0 lines of symmetry.

lines of symmetry = 0

Careful!

All three sides are different.

No fold makes the halves match.

Careful: not 1 ✗

Let's look back.

First: try the folds.

Last: count the lines.

Answer
lines of symmetry = 0

Your turn

Try this one yourself, then check:

Parallelogram: how many lines of symmetry?
Show the answer
lines of symmetry = 0

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