Question

in the diagram, \\( \frac { v z } { y z } = \frac { w z } { x z } \\).
to prove that \\( \triangle v w z \sim \triangle y x z \\) by the sas similarity
theorem, which other sides or angles should be used?
\\( \overline { w v } \\) and \\( \overline { x y } \\)
\\( \overline { w v } \\) and \\( \overline { z y } \\)
\\( \angle v z w \cong \angle y z x \\)
\\( \angle v w z \cong \angle y x z \\)

Explanation:

Step1: Recall SAS similarity theorem

SAS (Side - Angle - Side) similarity theorem states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the two triangles are similar.
We are given that \(\frac{VZ}{YZ}=\frac{WZ}{XZ}\). So we need to check the included angles for these sides.

Step2: Identify the included angles

For \(\triangle VWZ\) and \(\triangle YXZ\), the sides \(VZ\) and \(WZ\) in \(\triangle VWZ\) and \(YZ\) and \(XZ\) in \(\triangle YXZ\) have the included angles \(\angle VZW\) and \(\angle YZX\) respectively.

Answer:

\(\angle VZW\cong\angle YZX\)