Given that the triangles VWX and XYZ are isosceles, with angle WXV congruent to angle YZX, determine how the triangles can be shown to be similar.
A. Since WXV YZX and WV = WX, the triangles are similar by angle-side.
B. Since WXV YZX and WVX XYZ, the triangles are similar by angle-angle.
C. Since WXV YZX and WVX YXZ, the triangles are similar by angle-angle.
D. Since WXV YZX and YX = YZ, the triangles are similar by angle-side.
B. Since WXV ≅ YZX and WVX ≅ XYZ, the triangles are similar by angle-angle.
The correct answer is option B: Since WXV ≅ YZX and WVX ≅ XYZ, the triangles are similar by angle-angle.
In order for two triangles to be proven similar, the corresponding angles need to be congruent and the corresponding sides need to be proportional. In this case, only angle WXV ≅ angle YZX is given, which proves angle-angle similarity.
Option A is incorrect because angle WXV is given congruent to angle YZX, but there is no information about the sides WV and WX being proportional to the corresponding sides in the other triangle.
Option C is incorrect because although angle WXV ≅ angle YZX, there is no information about angle WVX ≅ angle YXZ being congruent.
Option D is incorrect because there is no information about side YX being proportional to side YZ in order to prove angle-side similarity.
To determine the similarity of triangles VWX and XYZ, we need to examine their angles and sides.
Given that triangles VWX and XYZ are isosceles, we know that VW = VX and XY = XZ. Additionally, we are given that angle WXV is congruent to angle YZX.
To determine the correct answer choice, we need to consider the three similarity criteria: angle-angle (AA), side-angle-side (SAS), and side-side-side (SSS).
Looking at the answer choices:
A. Since WXV ≅ YZX and WV = WX, the triangles are similar by angle-side.
B. Since WXV ≅ YZX and WVX ≅ XYZ, the triangles are similar by angle-angle.
C. Since WXV ≅ YZX and WVX ≅ YXZ, the triangles are similar by angle-angle.
D. Since WXV ≅ YZX and YX = YZ, the triangles are similar by angle-side.
Comparing the answer choices to the given information, we can see that option B aligns with the criteria for similarity. It states that WXV ≅ YZX and WVX ≅ XYZ, which satisfies the angle-angle similarity criterion.
Therefore, the correct answer is B. Triangles VWX and XYZ can be shown to be similar by angle-angle similarity.