To find: To explain why quadrilateral ABCD is a square by using the following condition, "Two congruent intersecting circles B and D (not shown) have a line (segment) of centers BD― and a common chord AC― that are congruent."

Question

To find:  To explain why quadrilateral ABCD is a square by using the following condition,  &quot;Two congruent intersecting circles B and D (not shown) have a line (segment) of centers BD― and a common chord AC― that are congruent.&quot;

Alix Ortiz · Accepted Answer

Given that circles B and D are congruent. Also centers BD― and a common chord AC― that are congruent.  That is =∼―AC―  The diagrammatic representation is given below,   Form the above circles AB=BC. Since radius of the circle B is same for all points on the circle.  Similarly, AD=DC  Also the circles B and D are congruent. Therefore, AB=BC=CD=DA  Then all the four sides are equal then ABCD is said to be rhombus.  Also given that the diagonals of ABCD are congruent. That is BD―=∼AC―  Hence ABCD is a square.  So, ABCD is a square.  Final statement:  The ABCD is a square.

To explain why quadrilateral ABCD is a square by

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