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Example: Find Missing Angles in Parallelogram

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Explanation:

 

 

Parallelogram

 

Parallelogram


This parallelogram is a rhomboid as its angles are oblique.

Type

quadrilateral

Edges and Vertices

4

Area

B × H;
ab sin θ

Properties

convex

 

In geometry, a parallelogram is a quadrilateral with two pairs of parallel sides. In Euclidean Geometry, the opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. (Our solved example in mathguru.com uses this concept)

The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean Parallel Postulate and neither condition can be proven without appealing to the Euclidean Parallel Postulate or one of its equivalent formulations. The three-dimensional counterpart of a parallelogram is a parallelepiped.

Properties

1.  Opposite sides of a parallelogram are parallel (by definition) and so will never intersect.

2.  Opposite sides of a parallelogram are equal in length. (congruent)

3.  Opposite angles of a parallelogram are equal in measure.

4.  Adjacent angles are supplementary (add up to 180 degrees). (Our solved example in mathguru.com uses this concept)

5.  The area of a parallelogram is twice the area of a triangle created by one of its diagonals.

6.  The area of a parallelogram is also equal to the magnitude of the vector cross product of two adjacent sides.

7.  The diagonals of a parallelogram bisect each other.

8.  Any line through the midpoint of a parallelogram bisects the area.

9.  Any non-degenerate affine transformation takes a parallelogram to another parallelogram.
There is an infinite number of affine transformations which take any given parallelogram to a square.

10.  A parallelogram has rotational symmetry of order 2 (through 180°). If it also has two lines of reflectional symmetry then it must be a rhombus or an oblong.

11.  The perimeter of a parallelogram is 2(a + b) where a and b are the lengths of adjacent sides.

12.  The sum of the squares of the sides equals the sum of the squares of the diagonals. This is the parallelogram law.

 

http://en.wikipedia.org/wiki/Parallelogram

 

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.