Question

a construction is illustrated below. your goal is to write three truths about the construction. choose all true statements. (overline{bz}) bisects (angle abc) (bx = by) (ba = by) (angle abzcongangle zbc)

Explanation:

Step1: Recall angle - bisector construction property

In an angle - bisector construction, the line that is constructed bisects the given angle. So, if $\overline{BZ}$ is the constructed line for $\angle ABC$, then $\overline{BZ}$ bisects $\angle ABC$, which means $\angle ABZ\cong\angle ZBC$.

Step2: Recall equal - distance property in construction

When constructing an angle - bisector, we use equal - radius arcs. When we start from point $B$ and draw arcs to intersect the sides of the angle, the lengths from the vertex $B$ to the intersection points on the sides of the angle (in this case $BX$ and $BY$) of the first - step arcs are equal, i.e., $BX = BY$.

Answer:

$\overline{BZ}$ bisects $\angle ABC$, $BX = BY$, $\angle ABZ\cong\angle ZBC$