Mathematics
Can you draw a triangle which has
(i) exactly one line of symmetry?
(ii) exactly two lines of symmetry?
(iii) exactly three lines of symmetry?
(iv) no lines of symmetry?
Sketch a rough figure in each case and name the triangle.
Answer
(i) Yes, a triangle with exactly one line of symmetry can be drawn. It is an isosceles triangle. The line of symmetry is the perpendicular from the vertex angle to the midpoint of the base.
(ii) No, a triangle with exactly two lines of symmetry cannot be drawn. Any triangle that has more than one line of symmetry must have all its sides and angles equal, which makes it an equilateral triangle (with 3 lines of symmetry).
(iii) Yes, a triangle with exactly three lines of symmetry can be drawn. It is an equilateral triangle. The three lines of symmetry are the perpendicular bisectors of its three sides (which are also the angle bisectors).
(iv) Yes, a triangle with no lines of symmetry can be drawn. It is a scalene triangle (all three sides of different lengths).
Related Questions
Copy the following figure on a squared paper and draw the lines of symmetry (if any) and count their number:
Write the letters of words 'JUST LOOK' which have no line of symmetry.
Copy the following figure on a squared paper. Complete each of them such that the dotted line is the line of symmetry:
Copy the following figure on a squared paper. Complete each of them such that the dotted line is the line of symmetry:
