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

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AB = CD (opposite sides)

Sum of all the four angles = 360 degrees

The crucial properties of angle of a parallel are:

If one angle of a parallelogram is a right angle, then all the angle are right anglesOpposite angles of a parallelogram space equal (or congruent)Consecutive angles space supplementary angles to each various other (that means they add up come 180 degrees)

Area that Parallelogram

Lines and also Angles course 7

Parallel present Transversals Angle

Perimeter of Parallelogram

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

## Opposite angle of a Parallelogram are equal

Theorem: Prove that the opposite angle of a parallelogram room equal.

Given: parallel 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 know that alternate interior angles are equal.

∠1 = ∠4

∠2 = ∠3

By ASA congruence criterion, 2 triangles are congruent to each other.

Therefore, ∠B = ∠D and also ∠A=∠C

Hence, the is showed that the opposite angles of a parallelogram are equal.

## Consecutive angle of a Parallelogram

Theorem: Prove that any kind of consecutive angles of a parallelogram are supplementary.

Given: parallel ABCD.

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

Proof: We recognize that inner angles ~ above the exact same side that a transversal space supplementary.

Therefore, ∠A + ∠D = 180°

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

Therefore, the sum of any type of two nearby angles of a parallel is same to 180°.

Hence, the is confirmed that any two adjacent or consecutive angle of a parallelogram are supplementary.

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If one angle is a appropriate angle, climate all 4 angles are ideal angles:

From the over theorem, it can be determined that if one angle of a parallel is a best angle (that is equal to 90 degrees), climate all four angles are best angles. Hence, the will become a rectangle.