Rhombus
Arhombusis aparallelogramwith fourcongruentsides. The plural of rhombus isrhombi. (I love that word.)
The formula for theareaof a rhombus is the same as the formula for a parallelogram:
,
whereis the length of a base andis the height.
.
Diagonals of a Rhombus
If a parallelogram is a rhombus, then its diagonals are perpendicular.
For Example:Ifis a rhombus, then.
If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.
For Example:Ifis a rhombus, then
.
Example 1:
In rhombus,. Find
In a rhombus, consecutive interior angles are supplementary. So,
.
Substitute the measures and solve for.
Use the value ofto find
Each pair of opposite angles of a rhombus is congruent. So,
.
Example 2:
In rhombus,. Find
The diagonals of a rhombus are perpendicular.
Use the Angle Sum Theorem.
Substitute the measures and solve.