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 letbe the common sidelength of Rhombusandbe 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 letbe the common sidelength of Rhombusandbe 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 RhombusRhombus.

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

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




Check:

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

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

Sincethen,

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

Since,

一个d

So,

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

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

Since angleis adjacent to angle, they must have a sum ofdegrees.

The solution is:

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

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

一个glesandare opposite interior angles, so they must have equivalent measurements.

The sum is:

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

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

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

一个gleand anglemust each equaldegrees. So the sum of anglesanddegrees.

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 thatmust be a right angle.