
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:
The required answer is
{{~m}~\angle 1}>{m}{{~\angle 2}}.
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