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Angles in a Parallelogram // Formula to Determine the Area of a Parallelogram // Geometry

Use Properties of Parallelograms:

A parallelogram is a quadrilateral with both pairs of opposite sides parallel. 





     Q.1. What is parallelogram?
Ans: The quadrilateral which opposite sides are equal and parallel is called a parallelogram.
Q.2. Formula to determine the area of a parallelogram.
Ans: Area = base x height
Q.3. What is the sum of 4 angles of a quadrilateral?
Ans: 360 degree
Q.4. Opposite sides of a quadrilateral are equal and parallel but angles are not right angle. It is called?
Ans: Parallelogram
Q.5. Where diagonals of a parallelogram bisect each other?
Ans: At intersecting point
Q.6. We measure angle in which unit?
Ans: Degree unit

There are four interior angles in a parallelogram and the sum of the interior angles of a parallelogram is always 360°. The opposite angles of a parallelogram are equal and the consecutive angles of a parallelogram are supplementary.
The amount of turn between two lines that meet each other.




The term "parallelogram PQRS" can be written as PQRS. In PQRS, PQII RS and QR II PS by definition. The theorems below describe other properties of parallelograms.





Parallelogram:
There are two pairs of parallel sides.
The opposite sides are equal in length.
Opposite angles are equal.
There are four interior angles in a parallelogram and the sum of the interior angles of a parallelogram is always 360°. The opposite angles of a parallelogram are equal and the consecutive angles of a parallelogram are supplementary.
Geometry Angles

Q. The figure shows a parallelogram ABCD where BAD = 64. E lies on AB such as ADE = 49.
Calculate
i) ABC
ii) CDE


Solution:
2 pairs of parallel sides
Opposite sides are equal in length
Opposite angles are equal
Diagonals bisect each other 
AE = DC,   AD = BC
i) ABC  + 64 = 180
ABC  = 180 - 64
            = 116 Ans.
ii) ADC  = 116
CDE + 49 = 116
CDE = 116 - 49
       = 67 Ans.

Angles in a Parallelogram:

                                There are 2 pairs of parallel sides.
                                  Opposite sides are equal in length
                                    Opposite angles are equal 

                                   i.e. ABC   = ABC
                                         BAD     =  BCD
                   DIAGONALS BISECT EACH OTHER
                                    AE = DC
                                    AD = BC

                   Q.1.  The figure shows a parallelogram ABCD where BAD = 64.  
                               E lies on AB  such that ADE  = 49.
                                 CALCULATE
                                    i) ABC
                                    ii) CDE

              Solution:
           I) ABC  +  64   =  180   (int.   AD//BC )
                     ABC    = 180 - 64
                                  = 116
           ii) ADC   = 116   ( opp.   )
                CDE  + 49    = 116
                 CDE   = 116 - 49
                            = 67   





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