Question

1. name a pair of congruent triangles. △ aob ≅ △ doc
2. state the triangle congruence postulate that shows the triangles are congruent.

(diagram: points a, b, o, c, d with $overline{ao} cong overline{od}$, $overline{bo} cong overline{oc}$, and tick marks on sides.)

Explanation:

Question 1

Step1: Identify given congruent sides and vertical angles

We know \( \overline{AO} \cong \overline{OD} \), \( \overline{BO} \cong \overline{OC} \), and \( \angle AOB \) and \( \angle DOC \) are vertical angles (so \( \angle AOB \cong \angle DOC \)).

Step2: Determine congruent triangles

By the Side - Angle - Side (SAS) congruence criterion, \( \triangle AOB \cong \triangle DOC \). Also, from the diagram, we can see that \( \overline{AB} \) and \( \overline{DC} \) related triangles, but the most direct pair from given markings is \( \triangle AOB \) and \( \triangle DOC \).

Step1: Recall triangle congruence postulates

The postulates are SAS (Side - Angle - Side), ASA (Angle - Side - Angle), SSS (Side - Side - Side), AAS (Angle - Angle - Side), HL (Hypotenuse - Leg for right triangles).

Step2: Match with given information

We have two sides (\( \overline{AO} \cong \overline{OD} \), \( \overline{BO} \cong \overline{OC} \)) and the included angle (\( \angle AOB \cong \angle DOC \) as vertical angles) equal. So the postulate is SAS.

Answer:

\( \triangle AOB \cong \triangle DOC \)

Question 2