Question

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

Explanation:

Step1: Recall Similar Triangles Property

Since \(\triangle YWZ \sim \triangle YXW\), corresponding angles are congruent. So, \(\angle WYZ=\angle XYW = 90^\circ\) (as \(WY\) is an altitude, forming right angles), and \(\angle YWZ=\angle YXW\), \(\angle YZW=\angle YWX\).

Step2: Analyze \(\angle XWZ\)

\(\angle XWZ\) is the right angle in \(\triangle WXZ\) because \(WY\) is an altitude, and from the similarity, the triangle \(\triangle WXZ\) must be a right triangle with \(\angle XWZ = 90^\circ\) (since corresponding angles in similar triangles and the right angle from the altitude imply \(\angle XWZ\) is a right angle).

Let's check other options:

• Option 1: Obtuse angle is wrong as it's a right angle.
• Option 3: \(\angle XWZ\) (right angle) and \(\angle WXY\) (acute) are not congruent.
• Option 4: \(\angle XWZ\) (right) and \(\angle XZW\) (acute) are not congruent.

Answer:

\(\boldsymbol{\angle XWZ}\) is a right angle. (The option: \(\angle XWZ\) is a right angle.)