MathematicsChoose given statement is true or false:State whether a transversal intersects two lines such that bisectors of a pair of corresponding angles are parallel,

Choose given statement is true or false:


State whether a transversal intersects two lines such that bisectors of a pair of corresponding angles are parallel,


  1. A
    True
  2. B
    False 

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    Solution:

    The given statement is True.
    Concept: Consider a line that, in this issue, crosses two other lines twice. Draw the bisectors of the respective angle that the line formed from these two points. We demonstrate the equality and correspondence of two pairs of angles using the bisectors property. The lines must be parallel if their respective angles are present. This process allows us to validate our conclusion.
    One helpful axiom for proving this result is “If a transversal intersects two lines such that a pair of corresponding angles is equal then the two lines are parallel to each other."
    The image shows that a transversal PQ crosses two lines, AB and CD, at their respective intersection locations E and G. E and G combine to form a pair of lines. The lines EF and GH serve as bisectors to the angles PEB and EGD, respectively.
    Since, EF acts as a bisector to the angle ∠PEB:
    ∠PEF=∠PEB
    Also, line GH acts a bisector to the angle ∠EGD:
    ∠EGH=∠EGD

    Now, EF and GH are parallel and PQ act as a transversal line, therefore by corresponding angle theorem,
    ∠PEF=∠EGH∴∠PEB=∠EGD

    Transversal and original line angles are therefore equivalent. They consequently become a pair of lines' equivalent angles.
    We can then deduce that lines AB and CD are parallel by applying the reverse of the equivalent angle axiom, which is presented at the top.
    Hence, the given statement is True.
     
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