Question

$△\mathbf{ABC}$and$△\mathbf{ABD}$ are congruent right triangles with common hypotenuse$\overline{\mathrm{AB}}$ . Write the theorem that allows you to conclude that point$\mathbf{B}$ lies on the bisector of$\angle \mathbf{DAC}$ .

Short answer

The theorem that conclude that point lies on the bisector of is that if a point is equidistant from the sides of an angle, then the point will lie on the bisector of the angle.

Step-by-step solution

- Definition of angle bisector.

The angle bisector of a given angle is the ray or segment that divides the given angle into two equal angles.

- Consider the diagram.

The figure is:

As,$△ABC$ and$△ABC$are the congruent triangles, therefore$\overline{BD}\cong \overline{BC}$ .

That implies the point$B$ is equidistant from the points D and C .

Therefore,$B$ lies on the bisector of$\angle DAC$ .

- Write the theorem that conclude that point lies on the bisector of .

The theorem that conclude that point lies on the bisector of is that if a point is equidistant from the sides of an angle, then the point will lie on the bisector of the angle.