Symmetry MCQ Test — Class 6 CBSE

Solution:

Step 1: Understand the definition of symmetry. A figure has symmetry if it can be divided by a line into two parts that are exactly alike.

Step 2: Consider the options. Option A describes this property perfectly: two identical mirror images.

Step 3: Options B, C, and D describe other properties (like passing through the center, connecting vertices, or equal area) which might be true for some lines but do not define a line of symmetry itself.

Solution:

Step 1: Recall the properties of an isosceles triangle. It has two equal sides and two equal base angles.

Step 2: To find a line of symmetry, we need a line that divides the triangle into two identical mirror images.

Step 3: The only way to achieve this for an isosceles triangle is by drawing a line from the vertex between the two equal sides to the midpoint of the base. This line bisects the vertex angle and is perpendicular to the base, creating two congruent right-angled triangles.

Step 4: Therefore, an isosceles triangle has exactly 1 line of symmetry.

Solution:

Step 1: A line of symmetry must divide a figure into two parts that are exact mirror images of each other. This means if you fold the figure along that line, the two halves should coincide perfectly.

Step 2: When a rectangle is folded along its diagonal, the two resulting triangles do not perfectly overlap. The corners do not align, showing they are not mirror images across that diagonal line.

Step 3: While the diagonal divides the rectangle into two congruent triangles (equal in size and shape), they are not mirror images in the context of reflectional symmetry along the diagonal itself. For example, a right angle on one side would not align with a right angle on the other side when folded along the diagonal.

Step 4: Therefore, Ravi is incorrect.

Solution:

Step 1: Understand reflection across a vertical line. A vertical line of symmetry acts like a mirror placed vertically.

Step 2: When an object is reflected across a vertical line, its image is inverted horizontally. Left becomes right, and right becomes left.

Step 3: If the letter 'L' (which opens to the right) is on the left side of the mirror line, its reflection on the right side will be a horizontally flipped version, which looks like a backwards 'L' (opening to the left).

Solution:

Step 1: A square is a regular polygon with four equal sides and four equal angles.

Step 2: Identify lines of symmetry that divide the square into identical mirror images.

Step 3: There are two lines of symmetry passing through the midpoints of opposite sides (one vertical, one horizontal).

Step 4: There are also two lines of symmetry passing through opposite vertices (the diagonals).

Step 5: In total, a square has 2 + 2 = 4 lines of symmetry.

Solution:

Step 1: Examine each letter for possible lines of symmetry.

Step 2: For 'F', no line (vertical or horizontal) divides it into identical mirror images.

Step 3: For 'A', a vertical line drawn through its peak and the midpoint of its base creates two identical mirror halves.

Step 4: For 'G' and 'P', no line (vertical or horizontal) divides them into identical mirror images.

Step 5: Therefore, 'A' has at least one line of symmetry.

Solution:

Step 1: Understand the types of symmetry mentioned. Rotational symmetry involves turning a figure around a point; translational symmetry involves sliding a figure; point symmetry involves rotation by 180 degrees.

Step 2: When we look in a plane mirror, the image we see is a 'mirror image' of ourselves.

Step 3: This phenomenon, where one half of a figure or object is the exact mirror image of the other half across a line (or plane), is known as reflective symmetry.

Step 4: Therefore, seeing our reflection in a plane mirror demonstrates reflective symmetry.

Solution:

Step 1: Recall the definition of symmetry. A figure is symmetrical if it can be divided into two halves that are exact mirror images of each other.

Step 2: For a rangoli pattern to be perfectly symmetrical across a central line, every element on one side of the line must have a corresponding, identical mirror image on the other side.

Step 3: Therefore, if one half is a floral pattern with five petals, the other half must be an exact mirror image of that same floral pattern with five petals.

Step 4: Options suggesting different patterns, random placement, or blank spaces would break the perfect symmetry.

Solution:

Step 1: A line of symmetry divides a figure into two identical mirror images.

Step 2: For a circle, any line that passes through its center divides it into two identical semicircles.

Step 3: Since there are infinitely many lines that can pass through the center of a circle, each of these lines acts as a line of symmetry.

Step 4: Therefore, a circle has an infinite number of lines of symmetry.

Solution:

Step 1: Recall the definitions of each figure and their lines of symmetry.

Step 2: An equilateral triangle has three equal sides and three equal angles, resulting in 3 lines of symmetry.

Step 3: A rectangle has two lines of symmetry (through the midpoints of opposite sides).

Step 4: A rhombus has four equal sides, and its diagonals are lines of symmetry, so it has 2 lines of symmetry.

Step 5: A scalene triangle has all three sides of different lengths and all three angles of different measures. Because of this lack of equality, no line can divide it into two identical mirror images.

Step 6: Therefore, a scalene triangle typically has no line of symmetry.