Question

prove that if one angle of a rhombus is a right angle the Rhombus is a square

Answer 1

Segment DA is congruent to segment AB.Segment CD is congruent to segment CB.Segment CA is congruent to segment CA.Triangle DAC is congruent to triangle BAC.Angle CAD is congruent to angle BAC. Angle DCA is congruent to angle ACB.Segment AC bisects angles BAD and DCB.

Then we will use only diagonal BD.

 



 

 

Segment DA is congruent to segment DC.Segment AB is congruent to segment BC.Segment BD is congruent to segment BD.Triangle DAB is congruent to triangle DCB.Angle ADB is congruent to angle BDC. Angle DBA is congruent to angle CBD.Segment BD bisects angles ADC and CBA.

Extension:

Transform the two-column proof into a paragraph proof.Find an alternative way to prove that the diagonals of a parallelogram bisect each other.