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    Mathematics
    Grade-8
    Easy

    Question

    Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

    1. AA
    2. SSS
    3. SAS
    4. no similar

    The correct answer is: AA

      The triangles are similar by AA.
      Because the triangles have at least two congruent angles.

      By angle sum property of a triangle ,we know that sum of interior angles of triangle is 180 degree
      So,
      In Triangle ANF :
      angle A N F space plus space angle N F A space plus space angle N A F space equals space 180 degree angle A N F space equals space 106 degree angle N A F space equals space 29 degree 106 degree space plus space 29 degree space plus space angle N F A space equals 180 degree angle N F A space equals space 180 degree space minus space 135 degree space equals space 45 degree
      Now comparing triangle ANF and EHS
      We can easily see they both have all angles same ,so by AA similarity they are similar triangle

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