Given that point U is the circumcenter of triangle XVZ, which segments are congruent?

By definition, when we say congruent, this means that the segment or sides have exactly the same length or identical. Based on the given figure above given that point U is the circumcenter of triangle XVZ, the segments that are segment UW, segment UY, and segment UA. Also segment UV and segment UZ. Hope this answer helps.

Answer Link

JeanaShupp JeanaShupp · Answer 2 · 2019-07-03T09:25:13+02:00

Answer: [tex]\overline{WX}\cong \overline{WV},\ \overline{VA}\cong\overline{AZ}[/tex]

[tex]\overline{XY}\cong\overline{YZ}[/tex]

[tex]\overline{UV}\cong \overline{UZ}\cong \overline{UX}[/tex]

Step-by-step explanation:

In the given figure we have a triangle , in which U is the circumcenter of triangle XVZ.

We know that the circumcenter is equidistant from each vertex of the triangle.

Since , the line segments which are representing the distance from the vertex and the circumcenter are [tex]\overline{UV},\ \overline{UZ},\ \overline{UX}[/tex]

Also, The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides.

Then , [tex]\overline{WX}\cong \overline{WV},\ \overline{VA}\cong\overline{AZ}[/tex] and [tex]\overline{XY}\cong\overline{YZ}[/tex]

Hence, the segments which are congruent are [tex]\overline{UV}\cong \overline{UZ}\cong \overline{UX}[/tex]

[tex]\overline{WX}\cong \overline{WV},\ \overline{VA}\cong\overline{AZ}[/tex]

[tex]\overline{XY}\cong\overline{YZ}[/tex]