Question

question 9 of 10
the assumption that \\( \overline { y z } \\) is a perpendicular bisector of \\( \overline { a x } \\) is not enough to show that \\( \triangle y x z \cong \triangle y a z \\).

a. true
b. false

Explanation:

Step1: Recall the definition of perpendicular bisector

If \( \overline{YZ} \) is a perpendicular bisector of \( \overline{XA} \), then \( XZ = AZ \) and \( \angle YZX=\angle YZA = 90^{\circ} \). Also, \( YZ = YZ \) (common side).

Step2: Apply the SAS (Side - Angle - Side) congruence criterion

In \( \triangle YXZ \) and \( \triangle YAZ \), we have \( XZ = AZ \) (from the perpendicular bisector property), \( \angle YZX=\angle YZA\) (right angles), and \( YZ = YZ \) (common side). By the SAS congruence criterion \( \triangle YXZ\cong\triangle YAZ\).

Answer:

B. False