Question

complete the two - column proof by selecting the correct postulate for reason two.
given: (overline{ab} cong overline{xy}), (overline{ac} cong overline{xz}), (overline{bc} cong overline{yz})
prove: (\triangle abc cong \triangle xyz)
proof:

statements	reasons

| 2. (\triangle abc cong \triangle xyz) | 2. select choice
postulate |

• aas
• sas
• sss
• hl

Explanation:

Step1: Recall Triangle Congruence Postulates

The SSS (Side - Side - Side) postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. The SAS (Side - Angle - Side) postulate requires two sides and the included angle to be congruent. AAS (Angle - Angle - Side) requires two angles and a non - included side. HL (Hypotenuse - Leg) is for right triangles.

Step2: Analyze Given Information

We are given that \(\overline{AB}\cong\overline{XY}\), \(\overline{AC}\cong\overline{XZ}\), and \(\overline{BC}\cong\overline{YZ}\). This means that all three corresponding sides of \(\triangle ABC\) and \(\triangle XYZ\) are congruent.

Step3: Match with Postulate

Since we have three pairs of congruent sides, the postulate that applies here is SSS.

Answer:

SSS (The option corresponding to SSS, for example, if the options are labeled as in the problem, the correct option is the one with SSS)