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To complete the congruence statement for the given triangles, we need to match the corresponding vertices of the two triangles based on their sides and angles.

Given triangles:

- Triangle \( \triangle DCE \)
- Triangle \( \triangle OPQ \)

By matching the corresponding sides and angles:

1. Angle \( D = 39^\circ \) corresponds to Angle \( O = 39^\circ \).
2. Angle \( C = 63^\circ \) corresponds to Angle \( P = 63^\circ \).
3. Angle \( E = 78^\circ \) corresponds to Angle \( Q = 78^\circ \).
4. Side \( DC = 49 \, \text{ft} \) corresponds to Side \( OP = 49 \, \text{ft} \).
5. Side \( CE = 31 \, \text{ft} \) corresponds to Side \( PQ = 31 \, \text{ft} \).
6. Side \( ED = 45 \, \text{ft} \) corresponds to Side \( QO = 45 \, \text{ft} \).

Thus, the corresponding vertices are:

- \( D \) corresponds to \( O \)
- \( C \) corresponds to \( P \)
- \( E \) corresponds to \( Q \)

Therefore, the complete congruence statement is:

\[
\triangle DCE \cong \triangle OPQ
\]

Would you like to discuss this further, or do you have any other questions?

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Here are some related questions:

1. How do you determine which angles correspond in congruent triangles?
2. What are the criteria for triangle congruence (SSS, SAS, ASA, etc.)?
3. Can congruent triangles have different orientations?
4. How do you prove triangles are congruent using coordinate geometry?
5. What is the significance of corresponding parts in congruent triangles?

**Tip:** Always match corresponding angles and sides carefully when identifying congruent triangles to ensure accuracy.

Complete the congruence statement for triangles DCE and OPQ.

Learn how to complete the congruence statement for triangles DCE and OPQ by matching corresponding angles and sides. This problem uses concepts of triangle congruence (ASA, SAS) and is suitable for students in Grades 8-10.

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