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Lelu [443]
3 years ago
11

Can anyone please help me with this.

Mathematics
2 answers:
geniusboy [140]3 years ago
5 0

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
stepladder [879]3 years ago
5 0

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}

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