8.
Congruent angles means congruent sides. In other words, equiangular triangles are also equilateral triangles.
9.
[tex]\begin{array}{l|l}{\underline {Statement} &\underline{Reason}\\1.\ \triangle JKM \text{is equilangular}&1.\ \text{Given}\\2.\ \angle J \cong \angle K \cong \angle M&2.\ \text{De-finition of Equiangular}\\3.\ IE \perp MK&3.\ \text{Given}\\4.\ \angle IEK\ \text{and}\ \angle IEM\ \text{are right angles}&4.\ \text{De-finition of Perpendicular}\\5.\ \angle IEK \cong \angle IEM&5.\ \text{Transitive Property}\\6.\ IE \cong IE&6.\ \text{Reflexive Property}\\\end{array}[/tex]
[tex]\begin{array}{l|l}\\7.\ \angle EIK\ \text{and}\ \angle EIM\qquad \qquad \qquad \quad&7.\ \text{Triangle Sum Theorem}\\8.\ \angle EIK \cong \angle EIM&8.\ \text{Transitive Property}\\9.\ \triangle IKE \cong \triangle IME&9.\ \text{Angle-Side-Angle Theorem}\end{array}[/tex]
