Chapter 2.5, Problem 7MRE

To determine

To conclude: From the given figure

Answer to Problem 7MRE

  $\overrightarrow{CG}\perp \overrightarrow{AD}$

Explanation of Solution

Given information:

  

  $\angle 4$ And $\angle 6$ are complements

  $\angle 4$ And $\angle 6$ are complements

When two lines intersect each other the opposite angles are called vertically opposite angles.

The angles are said to be complementary angle if the sum of the angle is ${90}^{\circ }$

Thus,

  $\angle 3=\angle 6$

Therefore, $\angle 3$ and $\angle 4$ are complements.

since,

  $\angle 3+\angle 4={90}^{\circ }$

Thus, the angle becomes:

  $\angle BCG={90}^{\circ }$

If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary.

Therefore,

  $\overrightarrow{CG}\perp \overrightarrow{AD}$