Given:
The figure of two triangle XYZ and UWV.
To find:
The theorem that is used to verify [tex]\Delta XYZ\sim \Delta UWV[/tex].
Solution:
In triangle XYZ,
[tex]m\angle X+m\angle Y+m\angle Z=180^\circ[/tex] (Angle sum property)
[tex]70^\circ+90^\circ+m\angle Z=180^\circ[/tex]
[tex]160^\circ+m\angle Z=180^\circ[/tex]
[tex]m\angle Z=180^\circ-160^\circ[/tex]
[tex]m\angle Z=20^\circ[/tex]
In triangle XYZ and triangle UWV,
[tex]m\angle Y\cong m\angle W[/tex] (Right angles)
[tex]m\angle Z\cong m\angle V[/tex] (Equal measures)
Two angles of one triangle are congruent to corresponding angles of another triangle. So, the triangles are similar by AA property of similarity.
[tex]\Delta XYZ\sim \Delta UWV[/tex] (AA similarity theorem)
Therefore, the correct option is B.
