On a line $l,$ take four points $A, B, C$ and $D$ in order such that $A B = C D$ . With the help of this figure, state whether $A C ≅ B D$ . Given resons to support your answer.

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Solution

Given that

$A B = C D$

Prove that $A C = B D$

Now, $A C = A B + B C . . . . (1)$

$B D = B C + C D . . . . . (2)$

By equation (1) - (2) to,

$A C - B D = (A B + B C) - (B C + C D)$

$= A B + B C - B C - C D$

$A C - B D = A B - C D$

given that,

$A B = C D$

$A C - B D = C D - C D$

$A C - B D = 0$

$A C = B D$ Hence, this is the answer.

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