Question

If line segment AB=line segment
PQ and line segment PQ=line segment
XY then relation between AB and XY IS​

Answer 1

Answer:

AB = XY line segment.

Step-by-step explanation:

As Line segment PQ = AB and also XY.

Hope this is right answer

Answer 2

Step-by-step explanation:

Given P is equidistant from points A and B

PA=PB       (1)

and Q is equidistant from points A and B

QA=QB       (2)

In △PAQ and △PBQ

AP=BP  from (1)

AQ=BQ from (2)

PQ=PQ  (common)

So, △PAQ≅△PBQ  (SSS congruence)

Hence ∠APQ=∠BPQ by CPCT

In △PAC and △PBC

AP=BP from (1)

∠APC=∠BPC from (3)

PC=PC  (common)

△PAC≅△PBC  (SAS congruence)

∴AC=BC by CPCT

and ∠ACP=∠BCP by CPCT   ....(4)

Since, AB is a line segment,

∠ACP+∠BCP=180

(linear pair)

∠ACP+∠ACP=180  °

from (4)

2∠ACP=180°

 ∠ACP=  2 180 °

=90°

Thus, AC=BC and ∠ACP=∠BCP=90°

∴,PQ is perpendicular bisector of AB.

Hence proved.