Question

use △xyz below to answer the question that follows: image of triangle xyz with point v on xz and point w on zy, and segment vw which fact is not used to prove that xyz is similar to vyw? (2 points) option 1: angle y is congruent to itself due to the reflexive property. option 2: angles zxy and wvy are congruent due to the corresponding angles theorem. option 3: x, v, and y are collinear points. option 4: xy is a transversal line passing vw and xz.

Explanation:

Step1: Analyze the first option

Angle \(Y\) is congruent to itself (reflexive property). This is used in proving similarity (AA similarity - if two angles of one triangle are equal to two angles of another triangle, the triangles are similar).

Step2: Analyze the second option

If \(WX\parallel XZ\) (assuming the parallel - line condition for the corresponding angles), angles \(ZXV\) and \(WVY\) are congruent (Corresponding Angles Theorem). This is also used in AA similarity.

Step3: Analyze the third option

\(X, V,\) and \(Y\) being collinear points is just a positional fact and does not contribute to the angle - angle similarity proof (which is based on angle congruence).

Step4: Analyze the fourth option

\(XY\) being a transversal passing \(WX\) and \(XZ\) is relevant for establishing angle congruence (using Corresponding Angles Theorem as in step 2) which is used in similarity proof.

Answer:

\(X, V,\) and \(Y\) are collinear points.