Question

1. complete the proof.

given: \\( \overline { a c } \cong \overline { a r } \\) and \\( \angle 1 \cong \angle 2 \\)
prove: \\( \angle 3 \cong \angle 4 \\)

1. given: \\( w x \parallel y z , \overline { w x } \cong \overline { y z } \\)

prove: \\( \delta w x z \cong \delta y z x \\)

Explanation:

Step1: Vertical angles are congruent

$$\angle LAC=\angle SAR$$

Step2: Use ASA (Angle - Side - Angle) criterion

Since $\overline{AC}\cong\overline{AR}$, $\angle 1\cong\angle 2$, and $\angle LAC=\angle SAR$, by ASA, $\triangle LAC\cong\triangle SAR$.

Step3: Corresponding parts of congruent triangles are congruent

If $\triangle LAC\cong\triangle SAR$, then $\angle 3\cong\angle 4$.

Answer:

$\angle 3\cong\angle 4$