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This is a two-column proof where the goal is to prove that the triangles \( \triangle ACB \) and \( \triangle ADB \) are congruent.

Let's go through it step by step:

### Step 1
- **Statements:** \( CA \cong DA \), \( CB \cong DB \)
- **Reason:** Given. These are given equalities based on the diagram, which shows that the sides of the rhombus are congruent.

### Step 2
- **Statements:** \( AB \cong AB \)
- **Reason:** Reflexive Property of Congruence. The side \( AB \) is congruent to itself since every segment is congruent to itself.

### Step 3
- **Statements:** \( \angle CAB \cong \angle DAB \) and \( \angle C \cong \angle D \)
- **Reason:** Given. These are given as part of the problem, showing that the angles between corresponding sides are equal.

### Step 4
- **Statements:** \( \angle CBA \cong \angle DBA \)
- **Reason:** Vertical Angles Theorem. Vertical angles formed by the intersection of lines are always congruent.

### Step 5
- **Statements:** \( \triangle ACB \cong \triangle ADB \)
- **Reason:** SAS (Side-Angle-Side) Congruence Postulate. We have shown two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.

Would you like more details or have any further questions?

Here are five related questions to deepen your understanding:
1. What is the importance of the SAS postulate in proving triangle congruence?
2. How do you identify vertical angles in geometric proofs?
3. Can the reflexive property be used for angles as well as sides?
4. What is the role of the given information in constructing a two-column proof?
5. How can congruent triangles help in solving for unknown angles or side lengths?

**Tip:** When doing geometry proofs, always look for properties like the Reflexive Property, Vertical Angles Theorem, and congruence postulates like SAS, SSS, or ASA to guide you through the reasoning process.

Complete the two-column proof by filling in the blanks. Prove that the triangles, shown in the figure to the right, are congruent.

Solve a two-column proof showing that two triangles are congruent using the SAS Congruence Postulate and the Vertical Angles Theorem. The proof walks through each statement and reason to complete the congruence proof. Ideal for students in Grades 8-10.

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