Question

Which would not be sufficient to prove WXZ ~ WYX?

Answer 1

An information that would not be sufficient to prove ΔWXZ ~ ΔWYX is: J. WZ/WX = XZ/XY = WX/WY.

In Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

The Side-Angle-Side (SAS) congruence theorem states that two (2) sides and the included angle of a triangle must be equal to the two (2) sides and one angle of the other triangle respectively.

Based on the side, angle, side (SAS) similarity theorem, we can logically deduce that ∆WXZ is congruent to ∆WYX when the angles WXZ and Y are congruent.

WZ/WX = XW/YW

WX/WZ =XY/ZX

m∠WXZ ≅ m∠Y

ΔWXZ ≅ ΔWYX

Answer 2

The Solution:

Given the figure below:

We are to identify the option that is not sufficient to prove that:

`\Delta WXZ\cong\Delta WYX`

Clearly, option H is not sufficient.

`\begin{gathered} \angle WXZ\cong\angle Y\text{ is not sufficient since} \\ \angle WXY\\e\angle\text{WZX}=90^o \end{gathered}`

Therefore, the correct answer is [option H]