A ** rhombus ** is a parallel with four congruent sides. The many of rhombus is ** rhombi ** . (I love the word.)

The formula for the area the a rhombus is the exact same as the formula for a parallelogram:

A = b h ,

where b is the size of a base and h is the height.

Area = 5 ⋅ 4 = 20 cm 2 .

### Diagonals that a Rhombus

If a parallel is a rhombus, climate its diagonals are perpendicular.

** because that Example: ** If ns Q R S is a rhombus, climate p R ¯ ⊥ Q S ¯ .

If a parallelogram is a rhombus, then each diagonal line bisects a pair of the opposite angles.

** because that Example: ** If p Q R S is a rhombus, then

∠ 1 ≅ ∠ 2 , ∠ 3 ≅ ∠ 4 , ∠ 5 ≅ ∠ 6 , and also ∠ 7 ≅ ∠ 8 .

** example 1: **

In rhombus A B C D , m ∠ A B C = 2 x − 7 and m ∠ B C D = 2 x + 3 . Find m ∠ D A B .

In a rhombus, consecutive internal angles are supplementary. So,

m ∠ A B C + m ∠ B C D = 180 ° .

instead of the measures and also solve because that x .

2 x − 7 + 2 x + 3 = 180 ° 4 x = 184 x = 46

use the value of x to find m ∠ D A B .

each pair that opposite angle of a rhombus is congruent. So,

m ∠ D A B = m ∠ B C D = 2 ( 46 ) + 3 = 95 ° .

** example 2: **

In rhombus X Y Z W , m ∠ W Y Z = 63 ° . Uncover m ∠ Y Z V .

The diagonals of a rhombus are perpendicular.

So, m ∠ Y V Z = 90 ° and also Δ Y V Z isarighttriangle .

usage the Angle amount Theorem.

m ∠ Y Z V + m ∠ Z V Y + m ∠ V Y Z = 180 °

substitute the measures and solve.

m ∠ Y Z V + 90 ° + 63 ° = 180 °

m ∠ Y Z V + 153 ° = 180 ° m ∠ Y Z V = 27 °

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