Chapter 4.1, Problem 11CE

To determine

To explain: the deduction method of $\overline{DA}\perp \overline{BA}$ from $\overline{DB}\perp \overline{DC}$ .

Answer to Problem 11CE

Explanation of Solution

Given information:

Suppose $\overline{DB}\perp \overline{DC}$ .

  

Calculation:

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.

  

The two triangles shown in the figure are congruent.

If their vertices superpose, then get:

  $\Delta AOB\cong \Delta COD$

Since, corresponding parts of congruent triangles are congruent.

Therefore,

  $\angle D\cong \angle B$

If $\overline{DB}\perp \overline{DC}$ , then

  $m\angle D=90°$

Therefore,

  $m\angle B=90°$

This implies,

  $\overline{DB}\perp \overline{BA}$