To write a congruency statement based on the information you've provided, we need to identify which triangles or figures are congruent. Given the angles and side lengths, we have:
- \( XY = 8 \)
- \( CD = 8 \)
- \( \angle X = 87^\circ \)
- \( \angle Z = 57^\circ \)
- \( \angle D = 36^\circ \)
- \( \angle B = 57^\circ \)
From this information, we can deduce that triangles that can be considered congruent must have equal corresponding sides and angles. Notably, we have:
- Two pairs of angles that are equal: \( \angle Z \) and \( \angle B \) both equal \( 57^\circ \).
- If \( \angle D = 36^\circ \) corresponds to another angle in the first triangle, we can also find that the last angle \( \angle Y \) should satisfy the triangle sum theorem.
To clearly write a congruency statement, further details about the triangles themselves are necessary (e.g., which triangle is which). Assuming we denote two triangles as \( \triangle XYZ \) and \( \triangle BCD \):
If we determine that \( \triangle XYZ \) and \( \triangle BCD \) have corresponding angles and sides, we could express their congruency like this:
\[ \triangle XYZ = \triangle BCD \]
This statement indicates that the two triangles are congruent based on the provided measures. If you could provide more context regarding the orientation or relationships between the angles and sides, a more specific congruency statement could be crafted.
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