Question

Complete.

If $△BAD\cong △TOP$, then role="math" localid="1649245739017" $\overline{DB}\cong \underset{\_}{?}$and role="math" localid="1649245766553" $△PTO\cong \underset{\_}{?}$.

Short answer

The complete statement is: If $△BAD\cong △TOP$, then $\overline{DB}\cong \overline{\mathrm{PT}}$and $△PTO\cong △\mathbf{DBA}$.

Step-by-step solution

Step 1. Description of step.

It is being given that $△BAD\cong △TOP$.

Therefore, the triangles $△BAD$and$△TOP$ are the congruent triangles.

When the two triangles are congruent, then the corresponding angles and corresponding sides of the triangles are congruent.

Step 2. Description of step.

As, $△BAD\cong △TOP$, therefore the corresponding angles and corresponding sides of the triangles$△BAD$ and$△TOP$ are congruent.

Therefore,

$$\begin{gathered} \angle B\cong \angle T \\ \angle A\cong \angle O \\ \angle D\cong \angle P \end{gathered}$$

and

$\begin{array}{l}\overline{BA}\cong \overline{TO}\\ \overline{AD}\cong \overline{OP}\\ \overline{DB}\cong \overline{PT}\end{array}$

Step 3. Write the complete statement.

Therefore, it can be seen that $\overline{DB}\cong \overline{PT}$.

As, $\angle B\cong \angle T$,$\angle A\cong \angle O$and $\angle D\cong \angle P$, therefore it can be seen that $△PTO\cong △DBA$.

Therefore, the complete statement is: If $△BAD\cong △TOP$, then$\overline{DB}\cong \overline{PT}$ and $△PTO\cong △DBA$.