91Ó°ÊÓ

The given diagram is:

From the diagram, it can be noticed that:

$∠CDF=∠1$and$∠FDB=∠2$

The angle bisector theorem states that if $\stackrel{↔}{BX}$is the bisector of $∠ABC$, then $∠ABX=\frac{1}{2}∠ABC$and $∠XBC=\frac{1}{2}∠ABC$.

Given that$\stackrel{↔}{DF}$bisects$∠CDB$.

Therefore, by using the angle bisector theorem it is obtained that:

$∠CDF=\frac{1}{2}∠CDB$ and $∠FDB=\frac{1}{2}∠CDB$.

Therefore, by using the above relation it can be obtained that $∠CDF=∠FDB$.

As$∠CDF=∠1$ and $∠FDB=∠2$, therefore it can be deduced that $∠1=∠2$.

As the angles∠1 and∠2 have equal measure therefore the angles∠1 and∠2are congruent angles.

That implies, $∠1â‰\dots ∠2$.

Therefore, the name of the theorem that justifies the statement about the given diagram is angle bisector theorem.