Classify the quadrilateral shown. Explain your reasoning. Thank you for your help.

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baxthum8 | High School Teacher | (Level 3) Associate Educator

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The top edge and the bottom edge are equal in length because the 2 triangles are congruent by SAS.  The left edge and right edge are equal in length because the two triangles are also congruent by Side-Angle-Side.  So, opposite sides are congruent.  This could be a rhombus, square, parallelogram or rectangle.  However, the only quadrilaterals to have equal congruent diagonals that bisect each other are a rectangle and square.  Since there is nothing that proves that the pairs of consecutive vetical angles are congruent we don't know that all the triangles are congruent.  Therefore it must be a rectangle.