Rhombus: Properties and Shape
Sides, Angles and Diagonals
A rhombus is a type of parallelogram, and what distinguishes its shape is that all four of its sides are congruent. There are several formulas for the rhombus that have to do with its
Probalby the most famous rhombus out there is the baseball diamond. The distance between each base is the same, making the shape a rhombus!
What must be the value of x if side BA = 5x-11
and side AD = 6x-18?
Diagonals of a Rhombus
Is the four-sided shape below, MNOP, a rhombus? If not, classify the shape.
Anngles of a Rhombus
What is the measure of the following angles in rhombus ABCD?
ACD = 46 °
ABD = 44°
A generalization about the angles of a rhombus
You can think of a 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
What is the value of x if angle BCA = 3x -2 and angle ACD = 12 + x?
What is the value of x, given the angle measurements below?
Area of Rhombus
What is the area of HIJK?Putting It All Together
STAR is a rhombus. The measure of diagonals SA is 24 and the measure of TR is 10, what is the perimeter of this rhombus?
Ask yourself: What is true about the angles formed by the diagonals of a rhombus?
The angles, are perpendicular!
Now, what is true about the diagonals of all parallelograms?
The diagonals of parallelograms bisect each other.
ZA = 12
ZT = 5
What kind of triangle is ZTA?
A Right Triangle!
So you can use the pythagorean theorem to find the measure of side TA
Now, that you know the length of TA? How can you use the fact that the sides of a rhombus are congruent to finish this problem?
Since, all 4 sides must be 13. The perimeter = 13 + 13 + 13 +13 = 52