Properties of Rhombi

Definition: A rhombus is a quadrilateral with four congruent sides.

All rhombi are parallelograms with the following properties:

– Diagonals are perpendicular, bisect each other, and bisect the interior angles
– All four sides are congruent
– Opposite angles are congruent
– Consecutive angles are supplementary

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Example: Find the length of diagonal AC if MC = 6 and DCBA is a rhombus.

rhombus.JPG

Solution: 

Use the given information and the properties of rhombi to determine the length of diagonal AC.

Step 1: We know segment MC = 6, and quadrilateral DCBA is a rhombus.

Step 2: Since the diagonals of a rhombus bisect each other, we know segment MC is equal to segment AM.
Segment AM must equal 6.

Step 3: If AM and MC are congruent segments both equal to 6, we can conclude that diagonal AC is equal to 12.
AC = 12

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