High School

Thank you for visiting On a coordinate plane a student transforms triangle UVW to form triangle XYZ The student correctly determines that tex UV XY tex tex m V. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

On a coordinate plane, a student transforms triangle UVW to form triangle XYZ. The student correctly determines that [tex]UV = XY[/tex], [tex]m∠V = m∠Y[/tex], and [tex]VW = YZ[/tex]. Which statement is true?

A) Triangle UVW must be congruent to triangle XYZ because there are two pairs of corresponding angles and the included side that are all congruent, so there is Side-Angle-Side congruence.

B) Triangle UVW must be congruent to triangle XYZ because there are two pairs of corresponding angles and the included side that are all congruent, so there is Side-Side-Angle congruence.

C) Triangle UVW must be congruent to triangle XYZ because there are two pairs of corresponding sides and the included angle that are all congruent, so there is Side-Angle-Side congruence.

D) Triangle UVW must be congruent to triangle XYZ because there are two pairs of corresponding sides and the included angle that are all congruent, so there is Side-Side-Angle congruence.

Answer :

Final answer:

Triangle UVW must be congruent to triangle XYZ because there are two pairs of corresponding sides (UV = XY, VW = YZ) and the included angle V in UVW corresponds with the angle Y in XYZ (m∠V=m∠Y). These criteria meet the Side-Angle-Side congruence rule, meaning the two triangles are congruent.

Explanation:

The correct statement is C) Triangle UVW must be congruent to triangle XYZ because there are two pairs of corresponding sides and the included angle that are all congruent, so there is Side-Angle-Side congruence. This is based on the theory of triangle congruence. When two triangles have two sides of equal length and the angle between these sides (the included angle) is also equal, the triangles are congruent through Side-Angle-Side (SAS) congruency. The side UV corresponds to XY and the side VW corresponds to YZ. The angle V (in triangle UVW) corresponds to the angle Y (in triangle XYZ). Therefore, since UV = XY, VW = YZ and m∠V = m∠Y, the triangles are congruent.

Learn more about Triangle Congruence here:

https://brainly.com/question/20521780

#SPJ11

Thank you for reading the article On a coordinate plane a student transforms triangle UVW to form triangle XYZ The student correctly determines that tex UV XY tex tex m V. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!

Rewritten by : Jeany

Other Questions