Question

use euclids to prove that if C lies between two points A and B such that AC=BC then prove that AC=1/2AB

Answer 1

If a point C lies between two points A and B such that AC = BC, then prove that AC =1/2AB. Explainby drawing the figure. 4. Ifa point C lies between two points A and B such that AC = BC, then prove that AC =1/2AB.
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Answer 2

hey dude !!!!

==>> Given = AC= BC ...............(i)

according to Euclid axioms " IF EQUALS ARE ADDED TO EQUAL THEN THE WHOLE WILL BE EQUAL"

AC+CB=BC+AC

according to Euclid axiom "THINGS WHICH COINCIDES WITH ONE ANOTHER"

AB=AC+BC ..............(ii)

according to Euclid axiom"THINGS WHICH ARE EQUAL TO SAME THINGS ARE EQUAL TO ONE ANOTHER "

by adding both the equations (i) and (ii) together..

we get ,

AB=AC+AC

AB=2AC

according to Euclid axiom " THINGS WHICH ARE HALVES OF THE SAME THINGS ARE EQUAL TO ONE ANOTHER "

therefore , 1/2AB =AC