Question

If A = B, B = C and C = D, which of the following is/are true?

• A. A = C
• B. B = D
• C. A + B = 3C
• D. A + C = 2D

Answer 1

Answer: (A), (B), (D)

The correct options are
A A = C
B B = D
D A + C = 2D

From Euclid's axioms, we know
"Things which are equal to the same things are equal to one another."
Given,
A = B and C = B.
Since A and C are equal to the same thing i.e., B, A = C.
Similarly,
D = C and B = C.
Since, D and B are equal to the same thing i.e C, B = D.
$\therefore$ A = B (given) and B = D (proved).
Again,
A = B and D = B,
Since, A and D are equal to the same thing i.e., B, A = D
$\therefore$ We can say,

• A = B
• B = C
• A = C
• B = D
• A = D

We know, if equals are added to equals, their wholes are equal.
$\therefore$ If we take A = D and C = D, we can say
A + C = D + D
$\Rightarrow$ A + C = 2D