ab is a line segment p and q are the points of opposite sides line AB such that each of the term equidistant form a and b show that a)triang

Question

ab is a line segment p and q are the points of opposite sides line AB such that each of the term equidistant form a and b show that a)triangles AQP congruent to BQP
b) triangle APC congruent to triangle BPC
c) PQ is the pendicular bisector of AB

in progress 0
4 weeks 2021-08-19T21:11:23+00:00 2 Answers 0 views 0

okk

Step-by-step explanation:

okkkkkkkkkkkkkkkkkkkkkkkk

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=  180/2

=90

Thus, AC=BC and ∠ACP=∠BCP=90

∴,PQ is perpendicular bisector of AB.

Hence proved.