Key words:
Consecutive
Summlementary
Bisect
Perpendicular
Congruent
Diagnals
Consecutive
Summlementary
Bisect
Perpendicular
Congruent
Diagnals
Rhombus:
Rhombus is a quadrolateral figure. Quadrolateral means a figure that has four sides. Rhombus has four equal sides like a square. But there is a difference between them. The difference is that a square has four angles that are 90 degrees. But a Rhombus has four angles that are less than a 90 degrees. when you compare diagrams of both figures they look like this:
Square 
RhombusAs you see the figures have similarities. All sides for both figures are equal. But all angles for both figures are not equal. Well, for the Rhombus two opposite angles are equal and less than 90 degrees and the other two opposite angles are equal and more than 90 degrees.
Consecutive angles are Suplementary in a Rhombus. Suplementary means that if you add the two consecutive angles the sum will be 180 degrees.
Example: if a Rhombus has four angles, ABCD. If angle B was 45 degrees what is the measure of the other angles?
1) angle B=45 degrees. that is equal to angle C, because in a Rhombus opposite angles are equal.
2) Since consecutive angles are Suplementary, angle A is consecutive to angle B.
180-45=135
angle A=135 degrees
3) opposite of angle A is angle D. Since opposite angles are equal in a rhombus, then angle D is 135 degrees.
The diagonals of a Rhombus bisect each other. what I mean by bisect each other is that they divide each other in to two equal pieces.
On the Rhombus above if ML=8cm and KN=5cm:
you can find how long MO is. This is how.
1) Since diagonals of a Rhombus bisect each other, 8 divide by 2 =4. So the length of MO=4cm.
2) diagonal KN is 5cm if it is bisected by side ML, side KO=2.5cm.
Diagonals of a Rhombus are perpendicular. Perpendicular is when the Diagonals cross each other and make a right angle triangle with one of the four sides of Rhombus.
If YW=5cm, if angle VWY was 42 degrees, and you are trying to find VW. Because the diagonals of a Rhombus are always Perpendicular you have a right angle triangle in the Rhombus above. So you are able to find side VW using the Cosine value to find VW.
cos 42=u/5
so VW would've been 3.7cm
Parallelogram:
Parallelogram is also one of the quadrolateral figures. It is more similar to rectangle than others. The only difference is that the 4 angle of the rectangle are 90 degrees and parallelogram has the two angles less than 90 degrees and the other two more than 90 degrees.
Parallelogram Rectangle
Consecutive angles of a Parallelogram are also sumplementary.
Example: if angle B in the Parallelogram ABCD below is 65 degrees, lets find the others.
Angle B=65 degrees
angle B=angle C, because in a Parallelogram opposite angles are equal.
Since consecutive angles in a Parallelogram are suplementary:
180-65=115
angle A and angle D are 115 degrees.
Diagonals of a Parallelogram bisect each other just like a Rhombus.
Example: if BC=20, you can find what BE is.
When we bisect(divide in half) BC in half, then we know that BE is 10. We also know that AE is 10, because in a Parallelogram the two diagonals are equal.
I hope my work helps. Thanks for reading.
