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.
You are watching: Consecutive angles in a parallelogram are always
AD = BC (opposite sides)
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
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
AB ∥ CD and advertisement is a transversal.
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.
See more: What Kind Of Dog Is Copper, The Fox And The Hound Dog Names
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.