A right triangle can have at most one line of symmetry.
Idea: A line of symmetry is a fold line that makes the shape overlap itself exactly.
Step 1: Understand right triangles
A right triangle has one angle equal to 90° (a right angle).
Step 2: When the two legs are different (scalene right triangle)
If the two shorter sides (legs) are not equal, folding along any line will not match both legs.
\(a \ne b\)
Reflecting swaps the legs, but their lengths are different, so shapes don’t overlap perfectly.
So, a scalene right triangle has no line of symmetry.
Step 3: When the two legs are equal (isosceles right triangle)
If the two legs are equal, there is exactly one fold line that works.
\(a = b\)
This line goes through the right-angle vertex and cuts the right angle into two equal 45° parts.
\(90^{\circ} = 45^{\circ} + 45^{\circ}\)
The same line is also the perpendicular bisector of the hypotenuse (it meets the hypotenuse at a right angle and at its midpoint).
\(\text{line} \perp \text{hypotenuse}\)
\(\text{line passes through midpoint}\)
So, an isosceles right triangle has exactly one line of symmetry.
Step 4: Can a right triangle have more than one line of symmetry?
No. Only an equilateral triangle has three symmetry lines, and an equilateral triangle cannot be right-angled.
Conclusion
Depending on side lengths, a right triangle has either 0 (scalene) or 1 (isosceles) line of symmetry. Therefore, a right triangle can have at most one line of symmetry.