Question

in this figure AB=BC,P is mid point of ab and Q is mid point of bc show that BP=BQ

Answer 1

P is mid point of AB
so , AP =BP ----- ( 1 )

also ,
Q is mid point of BC
so , BQ =CQ. ------ ( 2 )

AB = BC

but , AB = AP + BP

and BC = BQ + CQ

so , AP + BP = BQ + CQ

BP + BP = BQ + BQ ----- from 1 and 2

2 BP = 2 BQ

BP = BQ

Answer 2

Answer:

P is the midpoint of AB, so AP = BP — ( 1 )

Q is also BC's midpoint, 

therefore BQ = CQ. ——— (2)

AB = BC

nonetheless, AB = AP + BP.

, where BC = BQ + CQ

Therefore, AP + BP = BQ + CQ.

From 1 and 2, BP + BP = BQ + BQ

2 BP = 2 BQ

BP = BQ

Definition of Equidistant:

When a point is equally separated from two other points, it is said to be equidistant from both of them. For instance, a line segment's perpendicular bisector is equally spaced from both endpoints.

Equidistant, which implies at the same distance from a location, is another phrase for "equally distant." When two points are the same distance apart, they are said to be equally distant from one another. The term "equidistant" is most frequently used in the context of geometry when discussing parallel lines, perpendicular bisectors, circles, angle bisectors, and other similar concepts.

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