To determine which parallelogram is divided into two triangles that can be proven congruent by AAS (Angle-Angle-Side), let's consider the properties of a parallelogram:
- Opposite angles are equal.
- Adjacent angles are supplementary.
- The diagonals of a parallelogram bisect each other.
Typically, when a parallelogram is divided by its diagonal, two triangles are formed.
Given that the diagonals bisect each other, we can use the following arguments to show AAS congruence:
- Each triangle will share one angle (the angle between the sides of the parallelogram).
- The two angles adjacent to this common angle will be equal (due to the properties of the parallelogram).
- The side joining the two triangles is equal (since it's the same diagonal).
Thus, any parallelogram when split by its diagonals will meet the AAS criteria for congruency of the two triangles.
Therefore, all the parallelograms listed (WXYZ, JKLM, PQRS, ABCD) when divided by their diagonals will have the two resulting triangles that are congruent by AAS.
If you want to pick a specific one, it really doesn't matter which; all the options can enable AAS congruence for their divided triangles.
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