A square whose 2 pairs of sides are parallel to each and also the 4 angles at the vertices room not same to the right angle, climate the quadrilateral is called a parallelogram. Also, the opposite sides are equal in length.

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AB = CD (opposite sides)

Sum of all the four angles = 360 degrees

The important properties of angles of a parallel are:

If one angle of a parallelogram is a ideal angle, then every the angle are appropriate anglesOpposite angles of a parallelogram are equal (or congruent)Consecutive angles space supplementary angle to each other (that method they include up to 180 degrees)

Area the Parallelogram

Lines and also Angles course 7

Parallel present Transversals Angle

Perimeter that Parallelogram

## Opposite angles of a Parallelogram In the above parallelogram, A, C and B, D are a pair of the contrary angles.

## Opposite angles of a Parallelogram are equal

Theorem: Prove the the opposite angles of a parallelogram space equal.

Given: parallelogram ABCD.

To prove: ∠B = ∠D and also ∠A=∠C

Proof:

In the parallel ABCD,

AB \\ CD and ad \\ BC Consider triangle ABC and also triangle ADC,

AC = AC (common side)

We recognize that alternate interior angles space equal.

∠1 = ∠4

∠2 = ∠3

By ASA congruence criterion, two triangles room congruent to every other.

Therefore, ∠B = ∠D and also ∠A=∠C

Hence, the is confirmed that the opposite angle of a parallelogram space equal.

## Consecutive angles of a Parallelogram

Theorem: Prove that any type of consecutive angle of a parallelogram room supplementary.

Given: parallel ABCD.

To prove: ∠A + ∠B = 180 degrees, ∠C + ∠D = 180 degrees

Proof: We recognize that internal angles on the exact same side of a transversal are supplementary.

Therefore, ∠A + ∠D = 180°

Similarly, ∠B + ∠C = 180°, ∠C + ∠D = 180° and ∠A + ∠B = 180°.

Therefore, the amount of any kind of two adjacent angles the a parallel is equal to 180°.

Hence, it is proved that any kind of two surrounding or consecutive angles of a parallelogram space supplementary.

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If one angle is a appropriate angle, then all four angles are ideal angles:

From the over theorem, it deserve to be decided that if one edge of a parallelogram is a best angle (that is equal to 90 degrees), climate all four angles are best angles. Hence, that will end up being a rectangle.