Question

imilarity transformations
$overline{wy}$ is an altitude in triangle $wxz$.
if $\triangle ywz \sim \triangle yxw$, what is true about $\angle xwz?$
$\angle xwz$ is a right angle.
$\angle xwz$ is congruent to $\angle xzw$.
$\angle xwz$ is an obtuse angle.
$\angle xwz$ is congruent to $\angle wxy$.

Explanation:

Given \(\triangle YWZ \sim \triangle YXW\), corresponding angles of similar triangles are congruent. So \(\angle YWZ=\angle YXW\) and \(\angle YZW = \angle YWX\), and \(\angle Y=\angle Y = 90^\circ\) (since \(WY\) is an altitude, so \(\angle Y = 90^\circ\)). In \(\triangle WXZ\), we know that \(\angle XWZ\) should be a right angle because the sum of angles in a triangle is \(180^\circ\) and with the similar triangles' properties, we can deduce that \(\angle XWZ = 90^\circ\). The other options: \(\angle XWZ\) congruent to \(\angle XZW\) is not necessarily true, \(\angle XWZ\) being obtuse is wrong as we deduced it's right, and congruent to \(\angle WXY\) is also not correct from the similar triangles' angle correspondence.

Answer:

\(\angle XWZ\) is a right angle.