Question

if ∠1≅∠2, and ∠3≅∠2, then _____________.
your answer

if ∠j≅∠m, and ∠p≅∠m, then _____________.
your answer

if ∠a≅∠c, and ∠b≅∠c, then _____________.
your answer

if ∠6 is supplementary to ∠9, and ∠3 is supplementary to ∠9, then _____________.

Explanation:

Step1: Apply the transitive property of congruence

The transitive property of congruence states that if \(a\cong b\) and \(b\cong c\), then \(a\cong c\).
For \(\angle1\cong\angle2\) and \(\angle3\cong\angle2\), we substitute \(a = \angle1\), \(b=\angle2\), \(c = \angle3\) into the transitive property formula.
So \(\angle1\cong\angle3\).
For \(\angle J\cong\angle M\) and \(\angle P\cong\angle M\), substitute \(a=\angle J\), \(b = \angle M\), \(c=\angle P\) into the transitive property formula.
So \(\angle J\cong\angle P\).
For \(\angle A\cong\angle C\) and \(\angle B\cong\angle C\), substitute \(a=\angle A\), \(b=\angle C\), \(c=\angle B\) into the transitive property formula.
So \(\angle A\cong\angle B\).

Step2: Apply the congruent supplements theorem

The congruent supplements theorem states that if two angles are supplementary to the same angle (or to congruent angles), then the two angles are congruent.
Since \(\angle6\) is supplementary to \(\angle9\) and \(\angle3\) is supplementary to \(\angle9\), by the congruent supplements theorem \(\angle6\cong\angle3\).

Answer:

\(\angle1\cong\angle3\); \(\angle J\cong\angle P\); \(\angle A\cong\angle B\); \(\angle6\cong\angle3\)