Rhombus: Properties and Shape

Rhombus Sides

All sides of a Rhombus are congruent. Therefore, AB= BC = CD = AD

If side WX = 22, what is WZ?
 Side WZ  
WZ = 22

If side MN of rhombus LMNO is
X + 5 and side LM is 2x − 9, what must be the value of x?
 Answer  

What must be the value of x if side BA = 5x-11
and side AD = 6x-18?
 Answer  

Diagonals of a Rhombus

Diagonals are perpendicular.

• AOD = 90°
• AOB = 90°
• BOC = 90°
• COD = 90°

Is the four-sided shape below, MNOP, a rhombus? If not, classify the shape.
 Answer  
The shape below is not a rhombus because its diagonals are not perpendicular. However, since opposite sides are congruent and parallel, and the diagonals bisect each other. The shape below is a paralelogram.

Angles of a Rhombus

The diagonals bisect angles in each corner of a rhombus.
A proof of this property of the diagonals

What is the measure of the following angles in rhombus ABCD?
ACD = 46 °
ABD = 44°
 Answer  

A generalization about the angles of a rhombus

If you look at any rhombus as four triangles that are created by the diagonals such as , what is true about the outside angles in each triangle? An examples of outside angles are

Answer

Since the diagonals of a rhombs are perpendicular, these outside angles must be complementary angles.

What is the value of x if angle BCA = 3x -2 and angle ACD = 12 + x?
 Answer  

WHat is the value of x given the angle measurements below?
 Answer  

Area of Rhombus

The formula for area of this shape

Area = ½(diagonal₁ × diagonal₂)

What is the area of HIJK?
 Answer  
Area = ½(IK ×HJ) =½ (9 ×12) =54