Question

If ac = bd then prove that ab = cd

Answer 1

Answer:

Given, AC = BD......(1)

From the figure,

AC = AB + BC  &

BD = BC + CD

On putting these values in eq 1,

⇒ AB + BC = BC + CD

According to Euclid’s axiom, when equals are subtracted from equals, remainders are also equal.

On Subtracting BC from  both sides,

AB + BC – BC = BC + CD – BC

AB = CD                 [ by axiom 3 of Euclid]

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Answer 2

Answer:

Given, AC = BD......(1)

From the figure,

AC = AB + BC  &

BD = BC + CD

On putting these values in eq 1,

⇒ AB + BC = BC + CD

According to Euclid’s axiom, when equals are subtracted from equals, remainders are also equal.

On Subtracting BC from  both sides,

AB + BC – BC = BC + CD – BC

AB = CD                 [ by axiom 3 of Euclid]

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