Question

given: \\( \angle 2 \cong \angle 4 \\) prove: \\( \angle 1 \cong \angle 3 \\) 1 \\( \angle 2 \cong \angle 4 \\) given 2 \\( \angle 4 \cong \angle \square \\) select 3 \\( \angle 2 \cong \angle 3 \\) select 4 \\( \angle 1 \cong \angle \square \\) vertical angles property 5 \\( \angle 1 \cong \angle 3 \\) select

Explanation:

Step1: Vertical Angles Property

$\angle4\cong\angle3$ (Vertical Angles Property)

Step2: Transitive Property of Congruence

Since $\angle2\cong\angle4$ (Given) and $\angle4\cong\angle3$, by Transitive Property of Congruence, $\angle2\cong\angle3$

Step3: Vertical Angles Property

$\angle1\cong\angle2$ (Vertical Angles Property)

Step4: Transitive Property of Congruence

Since $\angle1\cong\angle2$ and $\angle2\cong\angle3$, by Transitive Property of Congruence, $\angle1\cong\angle3$

Answer:

1. $\angle3$; Reason: Vertical Angles Property
2. Reason: Transitive Property of Congruence
3. $\angle2$;
4. Reason: Transitive Property of Congruence