wy is an altitude in triangle wxz. if △ywz ~ △yxw, what is true about ∠xwz? ∠xwz is an obtuse angle. ∠xwz is…
wy is an altitude in triangle wxz. if △ywz ~ △yxw, what is true about ∠xwz? ∠xwz is an obtuse angle. ∠xwz is a right angle. ∠xwz is congruent to ∠wxy. ∠xwz is congruent to ∠xzw.
Answer
Explanation:
Step1: Recall similar - triangle properties
If (\triangle YWZ\sim\triangle YXW), then corresponding angles are equal.
Step2: Analyze angle - relationships
In (\triangle YWZ) and (\triangle YXW), (\angle WYZ=\angle XYW = 90^{\circ}) (since (WY) is an altitude). Also, (\angle WZY=\angle XWY) and (\angle YWZ=\angle YXW) because of similarity. We know that in (\triangle WXZ), (\angle XWZ=\angle XWY+\angle YWZ). In right - triangle (YWZ), (\angle WZY + \angle YWZ=90^{\circ}), and since (\angle WZY=\angle XWY), we have (\angle XWY+\angle YWZ = 90^{\circ}). So (\angle XWZ = 90^{\circ}).
Answer:
(\angle XWZ) is a right angle.