Olympiad Test: Symmetry - Class 7 MCQ

The letter H has both horizontal and vertical lines of symmetry.

• Horizontal symmetry: The top and bottom halves are mirror images.
• Vertical symmetry: The left and right halves are mirror images.

The mirror image of the letter 'W' when viewed in a vertical mirror is still 'W'. This is because:

• When a vertical mirror is used, the left and right sides of an object are reversed.
• The letter 'W' is symmetrical along a vertical axis, so its mirror image remains unchanged.

Solution:

• An equilateral triangle has all sides and angles equal, resulting in 3 lines of symmetry.

• An isosceles triangle has two sides and two angles equal, resulting in 1 line of symmetry.

• A scalene triangle has no equal sides or angles, so it has 0 lines of symmetry.

Therefore,Correct Answer - Option D.

A parallelogram has no lines of symmetry.

• Lines of symmetry are imaginary lines where you can fold the shape, and both halves match exactly.
• In a parallelogram, no such line exists that divides it into two identical parts.
• Unlike a square or rectangle, the angles and side lengths in a parallelogram do not allow for symmetry lines.

The letter A has line symmetry.

• A vertical line down its centre divides it into two identical halves.

• None of the other letters (P, Q, Z) have this symmetry.

An equilateral triangle is a triangle where all sides are equal.

• There is a line of symmetry from each vertex to the midpoint of the opposite side.
• Thus, an equilateral triangle has three lines of symmetry.

The letter V has a line of symmetry when reflected about a vertical mirror. Here's why:

• Symmetry means one half of the letter is a mirror image of the other half.
• For V, the left and right sides are identical when split vertically.
• Other letters like C, B, and Q do not have this property.

An isosceles triangle has specific symmetry properties:

• It has one line of symmetry.
• This symmetry line divides the triangle into two equal halves.
• The line runs from the vertex opposite the base to the midpoint of the base.

Thus, an isosceles triangle has one line of symmetry.

A rhombus has 2 lines of symmetry which cuts it into two identical parts. Both the lines of symmetry in a rhombus are from its diagonals. So, it can be said the rhombus lines of symmetry are its both diagonals.

A square has four lines of symmetry. These are:

• Two diagonals that intersect at the square's centre.
• Vertical line passing through the midpoints of the left and right sides.
• Horizontal line passing through the midpoints of the top and bottom sides.
• Each line divides the square into two symmetrical halves.