In Fig. AC=XD,C is the mid-point of AB and D is the mid-point of XY. Using a Euclid's axiom, show that AB=XY
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We have,
AC=XD and C as midpoint of AB & D as midpoint of XY
Clearly,AB=2AC and XY=2XD
Since,
AC=XD
AB=XY [double of equal things are equal to each other]
AC=XD and C as midpoint of AB & D as midpoint of XY
Clearly,AB=2AC and XY=2XD
Since,
AC=XD
AB=XY [double of equal things are equal to each other]
Answered by
12
Answer:
Since AC = XD, therefore AB = XY.
Step-by-step explanation:
Given two line segments, AB and XY.
C is the midpoint of AB and D is the midpoint of XY.
In geometry, the midpoint is the middle point of a line segment, that is equidistant from both the endpoints.
The midpoint on a line segment divides the segment into equal halves.
Hence, AB = 2AC and XY = 2XD
Given that the measures AC = XD
Euclid's axioms are the logical deductions in geometry proposed by Euclid.
According to Euclid's axiom, 'things which are double of the same things are equal to each other'.
Since, AC = XD
Therefore, AB = XY.
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