Question

In the following figure, the two-triangle shown are congruent. Then complete the following statement.

$\overline{AO}\cong \_\_\_$

Short answer

The statement is$\overline{\mathbf{A}\mathbf{O}}\mathbf{\cong }\overline{\mathbf{C}\mathbf{O}}.$

Step-by-step solution

Step 1. Apply the concept of congruent triangles.

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped, and turned to be looked identical.

Step 2. Check the figure.

Consider the figure.

Here the corresponding parts of$\Delta ABO$and$\Delta CDO$ are congruent such that their corresponding angles and sides are equal such that$\Delta ABO\cong \Delta CDO.$

Step 3. Step description.

Since two triangles are congruent then their corresponding angles and sides are equal, therefore$\overline{AO}\cong \overline{CO}.$

Therefore, the statement is$\overline{AO}\cong \overline{CO}.$