Question

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

Answer 1

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]

Answer 2

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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