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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AD = BC (opposite sides)
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
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
AB ∥ CD and advertisement is a transversal.
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.