Question

If WY and VX are perpendicular bisectores of one another at point Z, then which statement about the line segment is false?

a. XZ ~= ZV
b. VZ ~= ZX
c. WY ~= VX
d. WY _|_ VX

Answer 1

Each statement provided is true: XZ and ZV are equal, VZ and ZX are equal, WY and VX are equal in length, and WY is perpendicular to VX. There is no false statement given regarding the perpendicular bisectors WY and VX at point Z.

Step-by-step explanation:

If WY and VX are perpendicular bisectors of one another at point Z, it means that WZ = ZY and XZ = ZV. Since perpendicular bisectors not only intersect at a 90-degree angle but also bisect each other, then WY is equal to VX in length, and both WY and VX are perpendicular to each other.

Now, let's analyze the given statements:

• XZ ~= ZV: This statement is true because they are both bisected segments of VX, which means they are equal in length.
• VZ ~= ZX: This is just a reiteration of the previous statement where the order of the letters is reversed, so it is also true.
• WY ~= VX: This statement is true since WY and VX are equal in length, being bisected by Z.
• WY _|_ VX: This statement is true because WY and VX are perpendicular to one another by the definition of perpendicular bisectors.

Given the information provided, all statements are true. Thus, the original question asking for a false statement cannot be answered as such because no false statement is provided.