The figure given can be split into two triangles as shown;
The image shows two similar triangles.
Given:
That < X = < Y from the question.
WZ bisects angle XZY. This means it splits the angle into two equal parts.
Hence,
SInce angle X and angle Z in both triangles are equal, then the third angle W in both triangles will also be the same since the sum of angles in a triangle is 180 degrees.
hence,
Thus to make the two triangles look similar by flipping triangle WZY, we have;
From the image above, we can see that the two triangles are similar by angle, angle, angle (AAA).
Therefore, triangle XWZ and triangle YWZ are similar by AAA.
