Question

Can anyone please help me with this.

Answer 1

Answer:

Step-by-step explanation:

Givens

The triangle is equilateral.                         Given

<K = < M = 60                                             Property of an equilateral triangle.

IE = IE                                                           Reflexive property

Proof

• <IEK = <IEM  = 90                                  Property of perpendicular
• <EIK = 180 - 60 - 90                              All triangles have 180 degrees
• <EIK = 30                                               Subtraction
• <MIK = 180 - 60 - 90                             All triangles have 180 degrees
• <MIK = 30                                              Subtraction
• <MIE = <KIE                                           Both = 30 degrees
• IE = IE                                                     Reflexive property
• <IEK = <MEI                                            Both are right angles.
• ΔMIK ≡ΔKIE                                            ASA

Answer 2

8.

Congruent angles means congruent sides. In other words, equiangular triangles are also equilateral triangles.

9.

$\begin{array}{l|l}{\underline {Statement} &\underline{Reason}\\1.\ \triangle JKM \text{is equilangular}&1.\ \text{Given}\\2.\ \angle J \cong \angle K \cong \angle M&2.\ \text{De-finition of Equiangular}\\3.\ IE \perp MK&3.\ \text{Given}\\4.\ \angle IEK\ \text{and}\ \angle IEM\ \text{are right angles}&4.\ \text{De-finition of Perpendicular}\\5.\ \angle IEK \cong \angle IEM&5.\ \text{Transitive Property}\\6.\ IE \cong IE&6.\ \text{Reflexive Property}\\\end{array}$

$\begin{array}{l|l}\\7.\ \angle EIK\ \text{and}\ \angle EIM\qquad \qquad \qquad \quad&7.\ \text{Triangle Sum Theorem}\\8.\ \angle EIK \cong \angle EIM&8.\ \text{Transitive Property}\\9.\ \triangle IKE \cong \triangle IME&9.\ \text{Angle-Side-Angle Theorem}\end{array}$