Question

Given:$\mathbf{ABCD}$is a parallelogram;$\overline{\mathrm{AD}}\cong \overline{\mathrm{AC}}$;$\overline{\mathrm{AE}}\cong \overline{\mathrm{EC}}$;$\angle \mathbf{ADF}\cong \angle \mathbf{CDF}$;$\mathbf{m}\angle \mathbf{DAC}\mathbf{=}\mathbf{36}$.

Complete each statement about the diagram.

19.$\angle \mathbf{ADF}\cong \angle \mathbf{CDF}$, so$\overline{\mathrm{DF}}$ is a(n) of $\angle \mathbf{ADC}$.

Short answer

$\angle ADF\cong \angle CDF$, so $\overline{DF}$is an angle bisector of$\angle ADC$ .

Step-by-step solution

- Observe the given diagram.

The given diagram is:

- Write the definition of angle bisector.

The angle bisector is a ray which divides the given angle into two equal angles.

- Write the complete statement.

$\angle ADF\cong \angle CDF$, so$\overline{DF}$ is an angle bisector of$\angle ADC$ .