Question

using the image shown and xy = yz, answer true or false below. a. segment xz is longer than line w. b. x is an endpoint. c. line w is perpendicular to segment xz. d. line w is a bisector of xz.

Explanation:

Step1: Recall geometric definitions

A line extends infinitely in both directions, while a line - segment has two endpoints.

Step2: Analyze statement a

A line is infinite in length and a line - segment has a finite length. So, a line - segment XZ cannot be longer than an infinite line w. The statement "Segment XZ is longer than line w" is false.

Step3: Analyze statement b

From the figure, X is one of the endpoints of the line - segment XZ. So, the statement "X is an endpoint" is true.

Step4: Analyze statement c

There is no indication in the figure that the angle between line w and segment XZ is 90 degrees. So, the statement "Line w is perpendicular to segment XZ" is false.

Step5: Analyze statement d

Since XY = YZ, line w divides segment XZ into two equal parts. So, the statement "Line w is a bisector of XZ" is true.

Answer:

a. False
b. True
c. False
d. True