Question

Help! Given that WZ/YZ = VZ/XZ select the postulate theorem that you can use to conclude that the triangles are similar.

Answer 1

The pair of 'vertical' angles at point 'Z' that are inside the triangles are equal. 

Call me crazy, but I have a hunch:

Unless I miss my guess, there's a choice-(D) down below the
cut-off bottom of the picture, and that choice is "SAS similarity".

If I'm right, then that's your answer.

If I'm wrong, then you can delete my answer, and I'll mail back your 5 points.

Answer 2

Answer: SAS similarity theorem

Step-by-step explanation:

Given: $\frac{WZ}{YZ}=\frac{VZ}{XZ}$

Now from the given figure it can be seen that in ΔXYZ and ΔVWZ

∠WZY=∠WZY    [Vertically opposite angles are equal]

Also, $\frac{WZ}{YZ}=\frac{VZ}{XZ}$

Therefore by SAS criteria of similarity,  ΔXYZ and ΔVWZ are similar triangles.

• SAS similarity theorem says that if an angle of a triangle is equal to an angle of a another triangle and the lengths of the sides including these angles are proportional, then the triangles are similar.