Question

Can you conclude from the information given for the exercise that $\overrightarrow{XY}\perp \overrightarrow{XZ}$?

$\angle 1\cong \angle 4$and$\angle 2\cong \angle 3$

Short answer

The relation between the provided lines cannot be concluded.

Step-by-step solution

Step 1. Definition of congruent angles.

Angles having the same measurement are referred as the congruent angles.

Step 2. Definition of perpendicular lines.

The definition of perpendicular lines states that the relation between two lines is perpendicular when the property of angles formed by those lines represented by the congruent adjacent angles.

Step 3. Make the conclusion.

The definition of perpendicular line does not match with the relation between the provided angles because the provided relation between the angles is not true. So the relation between the provided lines cannot be concluded.