Question
(i) What letters of the English alphabet have reflection symmetry about:
a) A Vertical mirror
b) A Horizontal mirror
(ii) <Two friends arguing>
Suraj: If a figure can be folded along any line such that one half superimposes the other, it is known as a symmetric figure.
Ravi: If you can find a line in the figure which divides it into identical parts, then the figure is always symmetric.
Who is correct?
[4 MARKS]
a) A Vertical mirror
b) A Horizontal mirror
(ii) <Two friends arguing>
Suraj: If a figure can be folded along any line such that one half superimposes the other, it is known as a symmetric figure.
Ravi: If you can find a line in the figure which divides it into identical parts, then the figure is always symmetric.
Who is correct?
[4 MARKS]
Answer:
:
(i) Answer: 2 Marks
(ii) Answer: 2 Marks
a) Vertical mirror – A, H, I, M, O, T, U, V, W, X and Y
Horizontal mirror - B, C, D, E, H, I, O and X
(ii) If a figure can be folded along any line such that one half superimposes or aligns exactly with the other, it is known as a symmetric figure. For e.g. If you take a square and fold it across the line shown, part 1 exactly overlaps on part 2. So, the square is a symmetric figure.
On the other hand, in a parallelogram, the diagonal divides it into two congruent triangles (can be proven using SSS congruence condition), i.e. into two equal parts. But those parts don’t superimpose each other when folded across diagonal (as shown in the figure). So, the parallelogram is not symmetric.
Hence, Suraj is right and Ravi is wrong.
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:
(i) Answer: 2 Marks
(ii) Answer: 2 Marks
a) Vertical mirror – A, H, I, M, O, T, U, V, W, X and Y
Horizontal mirror - B, C, D, E, H, I, O and X
(ii) If a figure can be folded along any line such that one half superimposes or aligns exactly with the other, it is known as a symmetric figure. For e.g. If you take a square and fold it across the line shown, part 1 exactly overlaps on part 2. So, the square is a symmetric figure.
On the other hand, in a parallelogram, the diagonal divides it into two congruent triangles (can be proven using SSS congruence condition), i.e. into two equal parts. But those parts don’t superimpose each other when folded across diagonal (as shown in the figure). So, the parallelogram is not symmetric.
Hence, Suraj is right and Ravi is wrong.
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