Two figures are congruent by definition if all of their corresponding sides are congruent and all of their corresponding angles are congruent.

By definition, a rhombus has four sides of equal length.  If we let  be the common sidelength of Rhombus  and  be the common sidelength of Rhombus , then, since , it follows that , so corresponding sides are congruent. However, no information is given about their angle measures. Therefore, it cannot be determined whether or not the two rhombuses are congruent.

Two figures are similar by definition if all of their corresponding sides are proportional and all of their corresponding angles are congruent.

By definition, a rhombus has four sides that are congruent. If we let  be the common sidelength of Rhombus  and  be the common sidelength of Rhombus , it can easily be seen that the ratio of the length of each side of the former to that of the latter is the same ratio, namely, .

Also, a rhombus being a parallelogram, its opposite angles are congruent, and its consecutive angles are supplementary. Therefore, since , it follows that , and . By a similar argument,  and . Therefore, 

Since all corresponding sides are proportional and all corresponding angles are congruent, it holds that Rhombus  Rhombus .

The four interior angles in any rhombus must have a sum of  degrees. The opposite interior angles must be equivalent, and the adjacent angles have a sum of  degrees. 

Thus, if a rhombus has two interior angles of  degrees, there must also be two angles that equal: 




Check:

The four interior angles in any rhombus must have a sum of  degrees.

The opposite interior angles must be equivalent, and the adjacent angles have a sum of  degrees. 

Since  then, 

The four interior angles in any rhombus must have a sum of  degrees. The opposite interior angles must be equivalent, and the adjacent angles have a sum of  degrees. 

Since ,  

And  

So, 

The four interior angles in any rhombus must have a sum of  degrees.

The opposite interior angles must be equivalent, and the adjacent angles have a sum of  degrees. 

Since angle  is adjacent to angle , they must have a sum of  degrees. 

The solution is:

The four interior angles in any rhombus must have a sum of  degrees.

The opposite interior angles must be equivalent, and the adjacent angles have a sum of  degrees. 

Angles  and  are opposite interior angles, so they must have equivalent measurements.

The sum is:

The four interior angles in any rhombus must have a sum of  degrees.

The opposite interior angles must be equivalent, and the adjacent angles have a sum of  degrees. 

Since, both angles  and  are adjacent to angle --find the measurement of one of these two angles by: .

Angle  and angle  must each equal  degrees. So the sum of angles  and  degrees. 

A rhombus is defined to be a parallelogram with four congruent sides; there is no restriction as to the measures of the angles. Therefore, a rhombus can have angles of any measure. The correct choice is "false".

One characteristic of a rhombus is that its diagonals are perpendicular. It follows that  must be a right angle.