NCERT Exemplar Solutions Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - Fill in the Blanks
Question 42
Question. 42
A rectangle is symmetrical about the lines joining the _____ of the opposite sides.
Answer:
mid points.
Detailed Answer with Explanation:
Know the shapes and words
A rectangle has opposite sides equal and all angles are right angles (90°).
The midpoint of a side is the exact middle of that side.
A line of symmetry is a line that divides a shape into two matching (mirror) halves.
Name the rectangle
Let the rectangle be (ABCD) in order (so (AB) is opposite (CD), and (BC) is opposite (AD)).
Find midpoints on one pair of opposite sides
Let (M_1) be the midpoint of side (AB).
Let (M_2) be the midpoint of side (CD).
Join these midpoints
Draw the line (M_1M_2).
This line passes through the center of the rectangle and is parallel to the shorter pair of sides (if any).
Fold or mirror test (why it’s symmetry)
If you “fold” the rectangle along the line (M_1M_2):
– Points on the top half match exactly with points on the bottom half.
– Edges overlap perfectly.
Therefore, (M_1M_2) is a line of symmetry.
Repeat for the other pair of opposite sides
Let (N_1) be the midpoint of side (BC).
Let (N_2) be the midpoint of side (AD).
Draw the line (N_1N_2). By the same folding idea, (N_1N_2) is also a line of symmetry.
Important note
The diagonals of a rectangle are not lines of symmetry (unless the rectangle is a square).
Only the lines joining midpoints of opposite sides are symmetry lines for a general rectangle.
Conclusion
A rectangle has exactly two lines of symmetry: the lines joining the midpoints of each pair of opposite sides.