Question

Write the name or statement of the definition, postulate, or theorem that justifies the statement about the diagram.

$\mathbf{m}\mathbf{\angle }\mathbf{1}\mathbf{+}\mathbf{m}\mathbf{\angle }\mathbf{2}\mathbf{=}\mathbf{m}\mathbf{\angle }\mathbf{CDB}$

Short answer

The name of the postulate which justifies the statement about the given diagram is angle addition postulate.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

From the diagram, it can be noticed that:

$m\angle CDF=m\angle 1$and$m\angle FDB=m\angle 2$

Step 2. Write the angle addition postulate.

The angle addition postulate states that if point B lies in the interior of ∠AOC then $\mathbf{m}\mathbf{\angle }\mathbf{AOB}\mathbf{+}\mathbf{m}\mathbf{\angle }\mathbf{BOC}\mathbf{=}\mathbf{m}\mathbf{\angle }\mathbf{AOC}$.

Step 3. Write the name of the postulate that justifies the statement about the given diagram.

From the given diagram and the angle addition postulate it can be noticed that:

$$\begin{gathered} m\angle CDF+m\angle FDB=m\angle CDB \\ m\angle 1+m\angle 2=m\angle CDB \end{gathered}$$

Therefore, the name of the postulate that justifies the statement about the given diagram is the angle addition postulate.