Question

Statements: Segment Addition PostulateSubtraction Property of EqualityDefinition of segments (2nd use)Definition of segments (1st use)Substitution Property (2nd use)Symmetric PropertySubstitution Property (1st use) (Place statements to the right —->)

Answer 1

Given:

two-Proof are given and it should be named.

`\bar{1.VZ}\approx\bar{VY}\text{ and }\bar{\text{WY}}\approx\bar{XZ}`

Above proof is by Definition of segments.

`2.VZ=VY\text{ and WY}=XZ`

Above proof is by Definition of segments.

`3.\text{ }VZ=VX+XZ\text{ and VY=}VW+WY`

Above proof is by Segment of Addition Postulate.

`4.VX=XZ=VW+WY`

Above equation is wrong actually it is VX+XZ=VW+WY

and it is by Addition Property of Equality

`5.VX+WY=VW+WY`

Above equation is by Substitution Property (2nd use)

`6.VX=VW`

Above equation is by Substitution Property.