Chapter 4, Problem 20CR

To determine

To write: the theorem that allows concluding that point $B$ lies on the bisector of $\angle DAC$ .

Answer to Problem 20CR

If a point is equidistant from the sides of an angle, then the point lies of the bisector of the angle.

Explanation of Solution

Given information:

  $\Delta ABC$ and $\Delta ABD$ are congruent right triangles with common hypotenuse $\overline{AB}$ .

Calculation:

The bisector of an angle is the line or ray or segment passing through the vertex of the angle that divides it into equal angles.

  

In the above figure $\Delta ABC$ & $\Delta ABD$ are congruent right triangles with common hypotenuse $\overline{AB}$ . Therefore, the theorem which allows concluding that point $B$ lies on the bisector of $\angle DAC$ is given below:

If a point is equidistant from the sides of an angle, then the point lies of the bisector of the angle.