Question

Suppose you know that $\overline{DB}\perp \overline{DC}.$Explain how you can deduce that $\overline{DB}\perp \overline{BA}.$

Short answer

With the help of the congruency of$\mathit{\Delta }\mathit{A}\mathit{O}\mathit{B}\mathbf{\cong }\mathit{\Delta }\mathit{C}\mathit{O}\mathit{D},$$\overline{\mathbf{D}\mathbf{B}}\mathbf{\perp }\overline{\mathbf{B}\mathbf{A}}$can be explained.

Step-by-step solution

Step 1. Define concept of congruent triangles

The two triangles are said to be congruent if they are copies of each other and if their vertices are superposed, then can say that the corresponding angles and the sides of the triangles are congruent.

Step 2. Observe the figure

The two triangles shown in the figure are congruent.

Therefore, if their vertices are superposed, then $\Delta AOB\cong \Delta COD$ is obtained.

Step 3. Deduce DB perpendicular BA

Since $\Delta AOB\cong \Delta COD,$therefore, $\angle D\cong \angle B$because corresponding parts of congruent triangles are congruent.

Now it is given that $\overline{DB}\perp \overline{DC}$, then $m\angle D=90°$, and so $\overline{DB}\perp \overline{BA}$, which implies.

Therefore, with the help of the congruency of $\Delta AOB\cong \Delta COD$, $\overline{DB}\perp \overline{BA}$can be explained.