Mathematics

Question

please help thanks ❗​
please help thanks ❗​

1 Answer

  • Answer:

    see the explanation

    Step-by-step explanation:

    we know that

    The Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent

    Remember that if two triangles are congruent, then its corresponding angles and its corresponding sides are congruent

    In this problem

    PO≅SO ----> given problem

    NO≅TO ----> because O is the midpoint NT

    ∠PON≅∠SOT -----> by vertical angles

    so

    two sides and the included angle of triangle PON are congruent to two sides and the included angle of triangle SOT

    therefore

    Triangles PON and SOT are congruent by SAS

    hence

    ∠N≅∠T ----> by definition of congruence (corresponding angles are congruent)