Question

proof complete the two - column proof
given: ( ab cong xy ), ( ac cong xz ), ( bc cong yz )
prove: ( \triangle abc cong \triangle xyz )
proof:

statements	reasons
2. ( \triangle abc cong \triangle xyz )	2. select choice ( \boldsymbol{vee} ) postulate

(there is also a diagram of two triangles, ( \triangle abc ) and ( \triangle xyz ), with some markings on the sides.)

Explanation:

Step1: Identify Given Information

The given information is \( AB \cong XY \), \( AC \cong XZ \), \( BC \cong YZ \). These are the side - side - side (SSS) congruence criteria for triangles.

Step2: Apply SSS Congruence Postulate

The SSS (Side - Side - Side) Congruence Postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. For \( \triangle ABC \) and \( \triangle XYZ \), since \( AB\cong XY \), \( AC\cong XZ \), and \( BC\cong YZ \), by the SSS Congruence Postulate, \( \triangle ABC\cong\triangle XYZ \).

For the two - column proof:

• In the "Reasons" column for the second statement (\( \triangle ABC\cong\triangle XYZ \)), the reason is "SSS (Side - Side - Side) Congruence Postulate" because we have three pairs of congruent sides.

Answer:

For the reason of \( \triangle ABC\cong\triangle XYZ \) in the two - column proof, the reason is the SSS (Side - Side - Side) Congruence Postulate. So in the "Reasons" column for statement 2, we write "SSS Congruence Postulate".