Chapter 2.5, Problem 26WE

To determine

To conclude: The given diagram

Answer to Problem 26WE

Following can be concluded:

  $\overrightarrow{DA}\perp \overrightarrow{AC}$

  $\overrightarrow{EC}\perp \overrightarrow{AC}$

Explanation of Solution

Given information:

  

  $\begin{array}{l}\overrightarrow{AB}\text{bisects}\angle DAC\hfill \\ \overrightarrow{CB}\text{bisects}\angle ECA\hfill \\ m\angle 2={45}^{\circ }\hfill \\ m\angle 3={45}^{\circ }\hfill \end{array}$

The line is said to bisect the angle if it divides the angle into two equal parts.

And the right angle is an angle that make ${90}^{\circ }$ with the normal.

The angle $\angle DAC={90}^{\circ }$

Since, $\overrightarrow{AB}$ Bisects $\angle DAC$

Thus,

  $\angle 1=\angle 2={45}^{\circ }$

Therefore, $\angle 1+\angle 2={90}^{\circ }$

And hence,

  $\overrightarrow{DA}\perp \overrightarrow{AC}$

Similarly,

  $\overrightarrow{EC}\perp \overrightarrow{AC}$