Question

Use ΔXYZ below to answer the question that follows:

Triangle XYZ with sides YZ and YX intersected by line VW

Which fact is not used to prove that XYZ is similar to VYW?

A.) Angle Y is congruent to itself due to the reflexive property.
B.) Angles ZXY and WVY are congruent due to the Corresponding Angles Postulate.
C.) X, V, and Y are collinear points.
D.) XY is a transversal line passing VW and XZ.

Answer 1

Correct option is C.) X, V, and Y are collinear points.

Explanation:

Given ΔXYZ with sides YZ and YX intersected by line VW. we have to tell Which fact is not used to prove that XYZ is similar to VYW.

As we know the similarity rules, to prove the two triangles similar we need to prove angles or sides congruent or in proportion.

Option 1: The reflexive property showing an angle is congruent to itself helps to prove triangle congruent

Option 2: The Corresponding Angles Postulate helps to prove angles are congruent.

Option 3: A transversal can help prove angle congruence.

From all the given options, all the three options A,B and D are related to angles congruence, only the option 3 that is X, V, and Y are collinear points is the option which does not give any result with the help of that we can prove the angles or sides congruent or we can say triangles congruent.

Hence, the correct option is C.

Answer 2

The correct answer is:

C) X, V and Y are collinear points.

Explanation:

Three points being collinear does not do much in a similarity proof.

In order to prove similarity, we want to prove that all of the angles of one triangle are congruent to all of the angles of the other triangle.

The reflexive property showing an angle is congruent to itself helps do this.
The Corresponding Angles Postulate helps to prove angles are congruent.
A transversal can help prove angle congruence.

Collinear points will prove that angles sum to 180°, which will not help us prove similarity between triangles.