A \(30^\circ\)–\(60^\circ\)–\(90^\circ\) set-square has _____ line/lines of symmetry.
no.
39. A (30^circ)–(60^circ)–(90^circ) set-square has _____ line/lines of symmetry.
Answer: no.
What is a line of symmetry?
If you can fold a shape along a line and both halves match exactly, that line is called a line of symmetry.
What triangle are we talking about?
It’s a right triangle with angles:
(30^circ)
(60^circ)
(90^circ)
Check if any two angles are equal.
For symmetry in a triangle, usually at least two angles (and the opposite sides) are equal (like in an isosceles triangle).
Here we have three different angles:
(30^circ eq 60^circ)
(60^circ eq 90^circ)
(30^circ eq 90^circ)
So, no two angles are equal.
Look at the side lengths of a (30^circ)–(60^circ)–(90^circ) triangle.
Their ratio is:
(1 : sqrt{3} : 2)
All three sides are different.
Try possible folds and see if halves match.
Fold through the right angle (the (90^circ) vertex): one corner is (30^circ) and the other is (60^circ).
(30^circ eq 60^circ) → the corners won’t match after folding.
Fold through any other vertex: again you’ll try to match different angles/sides, so the halves won’t coincide.
Conclusion:
Because all angles and sides are unequal, there is no line along which the triangle can be folded to make two identical halves.
Therefore, number of lines of symmetry = (0).
Common mistake: Thinking every right triangle has a symmetry line. Only an isosceles right triangle (angles (45^circ), (45^circ), (90^circ)) has one line of symmetry. A (30^circ)–(60^circ)–(90^circ) triangle does not.