Question

In the diagram, StartFraction V Z Over Y Z EndFraction = StartFraction W Z Over X Z EndFraction. Triangles V W Z and Y X Z are connected at point Z. To prove that △VWZ ~ △YXZ by the SAS similarity theorem, which other sides or angles should be used? WV and XY WV and ZY ∠VZW ≅ ∠YZX ∠VWZ ≅ ∠YXZ

Answer 1

Answer:

Option C.

Step-by-step explanation:

It is given that

$\dfrac{VZ}{YZ}=\dfrac{WZ}{XZ}$

Triangles VWZ and YXZ are connected at point Z.  

According to SAS similarity theorem, two triangles are similar if two corresponding sides are proportional and the angles between proportional sides are equal.

To prove that △VWZ ~ △YXZ by the SAS similarity theorem, we have two corresponding proportional sides nd we need to find the angle between proportional sides.

In △VWZ and △YXZ, VZ and YZ, WZ and XZ are corresponding angles which are proportional.

Angle between VZ and WZ is ∠VZW.

Angle between YZ and XZ is ∠YZX.

So, △VWZ ~ △YXZ by the SAS similarity theorem if ∠VZW ≅ ∠YZX.

Therefore, the correct option is C.