Question

1. which of the following pieces of information would disprove that △mnp is similar to △xyz? a) ( mangle m

eq mangle z ) b) ( \frac{mn}{xy} = \frac{np}{yz} ) c) ( mangle n
eq mangle y ) d) ( \frac{mn}{xy}
eq \frac{xz}{mp} )

Explanation:

To determine which option disproves the similarity of \(\triangle MNP\) and \(\triangle XYZ\), we recall the criteria for triangle similarity (AA, SAS, SSS).

• Option A: \(m\angle M

eq m\angle Z\) – Similarity doesn't require \(\angle M\) to equal \(\angle Z\) (depends on correspondence), so this alone doesn't disprove similarity.

• Option B: \(\frac{MN}{XY} = \frac{NP}{YZ}\) – This is part of the SAS similarity criterion (if the included angle is equal). It supports, not disproves, similarity.
• Option C: \(m\angle N

eq m\angle Y\) – For SAS similarity, the included angle between the proportional sides must be equal. If \(\angle N\) (included between \(MN, NP\)) and \(\angle Y\) (included between \(XY, YZ\)) are not equal, SAS similarity fails. This directly disproves similarity.

• Option D: \(\frac{MN}{XY}

eq \frac{XZ}{MP}\) – These sides may not be corresponding, so this ratio inequality doesn't disprove similarity.

Answer:

C) \( m\angle N
eq m\angle Y \)