In `Delta ABC DEF` , AB=FD and `angleA=angleD`. The two triangle will be congruent by SAS axiom,if

Options

A. BC=EF
B. AC=DE
C. AC=EF
D. BC=DE

Explanation

To determine the conditions under which triangles ABC and DEF are congruent by the SAS (Side-Angle-Side) axiom, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- We have two triangles: Triangle ABC and Triangle DEF.
- It is given that AB = FD (one side of each triangle is equal).
- It is also given that ∠A = ∠D (the angle between the sides in each triangle is equal).

2. **Understanding SAS Congruence:**
- The SAS congruence criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

3. **Identify the Missing Side:**
- We have one side (AB = FD) and one angle (∠A = ∠D) given.
- To apply the SAS criterion, we need one more side. This side must be the side that is included between the two equal sides and the equal angles.

4. **State the Required Condition:**
- The required condition for the two triangles to be congruent by SAS is that the other sides, AC and DE, must be equal.
- Therefore, we need to establish that AC = DE.

5. **Conclusion:**
- The two triangles ABC and DEF will be congruent by the SAS axiom if AC = DE.

### Final Statement:
Thus, the two triangles will be congruent by the SAS axiom if AC = DE.

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