Question

the following statements were made:

1. connecting points u and t completes the construction of a bisector of ∠ytz.

ii. connecting points u and y completes the construction of a line parallel to line j through point y.
iii. connecting points u and z completes the construction of a line perpendicular to line j through point z.
which of the statements made are true?
o i only
o ii only
o i, ii, and iii
o i and ii

Explanation:

Step1: Recall angle - bisector construction

The steps of constructing an angle - bisector involve creating arcs from the vertex of the angle and then connecting the intersection of the arcs with the vertex. Connecting \(U\) and \(T\) follows the standard arc - based construction of an angle bisector for \(\angle YTZ\), so statement I is true.

Step2: Recall parallel - line construction

To construct a line parallel to a given line \(j\) through a point \(Y\), the construction typically involves using corresponding angles or alternate interior angles. The given construction does not follow the steps for constructing a parallel line by connecting \(U\) and \(Y\), so statement II is false.

Step3: Recall perpendicular - line construction

To construct a line perpendicular to a given line \(j\) through a point \(Z\), the construction usually involves creating arcs from \(Z\) and then connecting the intersection of the arcs. The given construction does not follow the steps for constructing a perpendicular line by connecting \(U\) and \(Z\), so statement III is false.

Answer:

I only