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Bilateral Symmetry

Find the numb...

Question

Find the number of lines of symmetry in each of the following shapes.

a-1, b-1, c-3

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a- 2, b-1, c-4

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a-3, b-2, c-1

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a-1, b-3, c-2

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Solution

The correct option is A
a-1, b-1, c-3

The christmas tree has one line of symmetry which is similar to the butterfly.
A snow flake has three lines of symmetry. The lines of symmetry for the figures are depicted below.

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Question 1(b)

Find the number of lines of symmetry for given shape:

a_{1} b_{1} c_{1}, a_{2} b_{2} c_{2}

a_{3} b_{3} c_{3}

Δ = ∣ ∣ ∣ ∣ \begin{matrix} c_{1} & a_{1} & b_{1} c_{2} & a_{2} & b_{2} c_{3} & a_{3} & b_{3} \end{matrix} ∣ ∣ ∣ ∣

Δ

x = 1 + a + a^{2} + a^{3} + . . . .

\infty (| a | < 1)

y = 1 + b + b^{2} + b^{3} + . . .

\infty (| b | < 1)

1 + a b + a^{2} b^{2} + a^{3} b^{3} + . . .

\infty = \frac{x y}{x + y - 1}

If a, b, c are in G.P., prove that:

(i) $a (b^{2} + c^{2}) = c (a^{2} + b^{2})$

(ii) $a^{2} b^{2} c^{2} (\frac{1}{a^{3}} + \frac{1}{b^{3}} + \frac{1}{c^{3}}) = a^{3} + b^{3} + c^{3}$

(iii) $\frac{(a + b + c)^{2}}{a^{2} + b^{2} + c^{2}} = \frac{a + b + c}{a - b + c}$

(iv) $\frac{1}{a^{2} - b^{2}} + \frac{1}{b^{2}} = \frac{1}{b^{2} - c^{2}}$

(v) $(a + 2 b + 2 c) (a - 2 b + 2 c) = a^{2} + 4 c^{2}$ .

\begin{matrix} 1. W e i g h t o f a b a n g l e & a . L i t r e 2. W a t e r i n a c a n & b . K i l o g r a m 3. B a g o f w h e a t & c . M i l l i g r a m \end{matrix}

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