Write an inequality relating the given pair of angle measures

Write an inequality relating the given pair of angle measures

Step By Step Solution:

Since AB=AD, the corresponding sides are congruent:

\overline{AB}\cong{\overline{AD}}

The segment AC is common to both triangle ACB and triangle ACD and, by the Reflexive Congruence Property, it follows:

\textcolor{primary}{\overline{AC}}\cong\textcolor{primary}{\overline{AC}}
Note :Here Reflexive Congruence Property means line AC is congruent to itself

Since, BC> CD from the Converse of the Hinge Theorem, for the sides opposite the included angles it follows:

\textcolor{primary}{m\angle CAB}\gt \textcolor{secondary}{m\angle CAD}

Substitute the value of

\textcolor{primary}{m\angle CAB}=\textcolor{primary}{m\angle 1}, \textcolor{secondary}{m\angle CAD} ={m}{\angle 2}

into the above expression, then we get:

\textcolor{primary}{m~\angle 1}\gt \textcolor{secondary}{m~\angle 2}

Required Solution:

{{~m}~\angle 1}>{m}{{~\angle 2}}.