Question

mathematics diagnostic assessment
prove that alternate interior angles 3 and 6 are congruent.
$\angle 2 \cong \angle 3$ $m\angle 5 = 180^{\circ} - m\angle 6$ corresponding angles are congruent.
transitive property of congruence $\angle 3 \cong \angle 6$ supplementary angles sum to $180^{\circ}$.
vertical angles are congruent.
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$$\begin{tabular}{|c|c|} \\hline statement & reason \\\\ \\hline $\\angle 2 \\cong \\angle 6$ & \\\\ \\hline & \\\\ \\hline & \\\\ \\hline \\end{tabular}$$

Explanation:

Step1: State first congruence

$\angle 2 \cong \angle 6$
Reason: Corresponding angles are congruent.

Step2: State vertical angle congruence

$\angle 2 \cong \angle 3$
Reason: Vertical angles are congruent.

Step3: Apply transitive property

$\angle 3 \cong \angle 6$
Reason: Transitive property of congruence.

Answer:

Statement	Reason
$\angle 2 \cong \angle 3$	Vertical angles are congruent.
$\angle 3 \cong \angle 6$	Transitive property of congruence.