Help with geometry please Classify the quadrilateral shown o

Classify the quadrilateral shown on the right. Explain your reasoning.

Solution

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.  

A square is a special kind of rectangle, it is one where all the sides have the same length. Thus every square is a rectangle because it is a quadrilateral with all four angles right angles. However not every rectangle is a square, to be a square its sides must have the same length.

Therefore the quadrilateral shown in the figure is a SQUARE.