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13 February, 04:38

Given : Segment AC is perpendicular to BD

Segment BD bisects segment AC

Prove: Triangle ABD is congruent to Triangle CBD

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Answers (1)
  1. 13 February, 04:58
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    Triangle ABD and CBD are congruent by the SAS postulate

    Step-by-step explanation:

    Step 1:

    Given,

    Segment AC is perpendicular to BD

    Segment BD bisects segment AC

    To prove the given two triangles are congruent

    Step 2:

    Since AC is perpendicular to BD, We have ∠BDA and ∠BDC to be equal to 90 degrees

    Also we have AD = DC, because BD bisects AC

    BD is a side common to both the triangles and hence is the same

    So we have two sides and angle between them (included angle) to be same for both the triangles.

    Hence Triangle ABD and CBD are congruent.
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