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

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

Answers ( )

  1. Ava
    0
    2021-08-19T21:12:34+00:00

    Answer:

    okk

    Step-by-step explanation:

    okkkkkkkkkkkkkkkkkkkkkkkk

    0
    2021-08-19T21:12:36+00:00

    Answer:

    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.

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