Explanation (Beginner-Friendly)
What is a line of symmetry?
- A line of symmetry is a fold line that splits a shape into two exactly matching halves.
- If you fold the shape on this line, both parts should overlap perfectly.
About a 30°–60°–90° triangle (set-square):
- It’s a right triangle with angles: \(30^circ\), \(60^circ\), and \(90^circ\).
- Its side lengths are in the ratio:
shortest side \(= a\)
longest side (hypotenuse) \(= 2a\)
third side \(= a\sqrt{3}\)
- Notice all three sides are different:
\(a\) is not equal to \(2a\),
\(a\) is not equal to \(a\sqrt{3}\),
and \(2a\) is not equal to \(a\sqrt{3}\).
Why this matters for symmetry:
- Only special triangles (like isosceles or equilateral) have mirror lines.
- An isosceles triangle has at least one pair of equal sides → it can have 1 line of symmetry.
- An equilateral triangle has 3 equal sides → it has 3 lines of symmetry.
- But a 30°–60°–90° triangle is scalene (all sides different) → no mirror line works.
Quick fold test (imagination):
- Try folding through the \(90^circ\) angle to split the triangle — the two halves won’t match.
- Try folding along any altitude or median — the sides and angles won’t pair up equally.
Conclusion: A 30°–60°–90° set-square has 0 lines of symmetry.
Answer: Option A — 0
Why the other options are wrong?
- 1: Would be true for an isosceles right triangle (\(45^circ\)–\(45^circ\)–\(90^circ\)), not for 30°–60°–90°.
- 2 or 3: Possible for more symmetric shapes (like equilateral triangles), not for a scalene triangle.