NCERT Solutions Class 6 Maths Chapter 11 — Symmetry

Solution:

Step 1: 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: Step 2: Consider the options. Option A describes this property perfectly: two identical mirror images.

Step 3: 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: Step 1: Recall the properties of an isosceles triangle. It has two equal sides and two equal base angles.

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

Step 3: 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: Step 4: Therefore, an isosceles triangle has exactly 1 line of symmetry.

Solution:

Step 1: 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: 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: 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: Step 4: Therefore, Ravi is incorrect.

Solution:

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

Step 2: 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: 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: Step 1: A square is a regular polygon with four equal sides and four equal angles.

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

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

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

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