To prove quadrilateral ABCD is a parallelogram, show that opposite sides AB and DC are both parallel (using angle properties) and congruent, meeting the definition of a parallelogram.
To establish that a quadrilateral ABCD is a parallelogram by demonstrating that a specific pair of opposite sides are both parallel and congruent, we can employ the properties of parallelograms.
Firstly, let's consider the definition of a parallelogram. A parallelogram is a quadrilateral with opposite sides that are both parallel and equal in length.
To demonstrate this in ABCD, we can focus on one pair of opposite sides, say AB and DC. If we can prove that AB is parallel to DC and that they are of equal length, we establish that ABCD is a parallelogram.
For parallelism, we can use the given information or other known properties of the figure, such as opposite angles being equal. If angles A and D are equal, it implies that AB is parallel to DC.
For congruence, we may use methods such as the measurement of side lengths or angle measurements. If AB is equal in length to DC, and we have established their parallelism, we confirm that ABCD is a parallelogram.
In conclusion, by demonstrating that opposite sides AB and DC are both parallel and congruent, we satisfy the criteria for a parallelogram, providing a rigorous proof of ABCD's parallelogram classification.
The question probable may be:
How can we establish that a quadrilateral ABCD is a parallelogram by demonstrating that a specific pair of opposite sides are both parallel and congruent?