https://file.aiquickdraw.com/mathbot/file/1726100767872l6jobws7.jpg

To prove that the given shapes (quadrilaterals) are congruent, we need to establish that their corresponding sides and angles are equal.

Looking at the diagram:

1. **Angles**: It appears that both quadrilaterals have the same pattern of angle markings. These markings suggest that:
   - \(\angle ONP = \angle WXY\)
   - \(\angle OPQ = \angle WXV\)
   - \(\angle PQO = \angle YVX\)
   - \(\angle QON = \angle XWV\)

   If the angles in both shapes are equal, the shapes could be congruent based on angle properties.

2. **Congruency criteria**:
   - For quadrilaterals, proving congruency often requires checking if two shapes satisfy the Angle-Side-Angle (ASA), Side-Angle-Side (SAS), or Side-Side-Side (SSS) congruence rules.
   - Here, based on the provided angle congruences, we may check whether there is enough information to apply ASA (since we already have corresponding equal angles).

However, the sides are not labeled, so unless there is more information (such as side lengths or additional relationships between the sides), we cannot definitively conclude that the shapes are congruent just from the angle markings alone.

### Conclusion:
- Based on the angle markings alone, we can say that the two shapes might be congruent by the Angle-Angle-Angle (AAA) criterion, which works only for triangles or when considering angles in isolation.
- For complete congruence, we'd need further information about the sides.

Would you like more detailed help, or do you want to discuss congruence in polygons further?

### Follow-up questions:
1. Are there specific side lengths or ratios given for the shapes?
2. Could you clarify if any additional congruence criteria, such as side lengths, are available?
3. Are the quadrilaterals supposed to be in similar configurations?
4. Can you identify any symmetrical properties between the quadrilaterals?
5. Would you like to explore how congruence criteria differ between triangles and polygons?

### Tip:
When working with polygons, matching angles alone can suggest similarity, but congruence usually requires equal sides too.

Can you prove these shapes are congruent?

Explore how to prove the congruence of quadrilaterals based on angle markings. Learn about the Angle-Angle-Angle (AAA) criterion and other congruence theorems that apply to polygons. Suitable for students in Grades 8-10.

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