raj correctly determined that ray lh is the bisector of ∠gli. which information could he have used to…

raj correctly determined that ray lh is the bisector of ∠gli. which information could he have used to determine this? ∠glh ≅ ∠ilm m∠klm = 5m∠ilm m∠gli = 2m∠glh m∠gli = 1/2m∠glh + 1/2m∠hli

raj correctly determined that ray lh is the bisector of ∠gli. which information could he have used to determine this? ∠glh ≅ ∠ilm m∠klm = 5m∠ilm m∠gli = 2m∠glh m∠gli = 1/2m∠glh + 1/2m∠hli

Answer

Explanation:

Step1: Recall angle - bisector definition

An angle - bisector divides an angle into two equal angles. If ray $LH$ is the bisector of $\angle GLI$, then $\angle GLH=\angle HLI$ and $m\angle GLI = m\angle GLH + m\angle HLI=2m\angle GLH = 2m\angle HLI$.

Step2: Analyze each option

  • Option 1: $\angle GLH\cong\angle ILM$ has no relation to the fact that $LH$ bisects $\angle GLI$.
  • Option 2: $m\angle KLM = 5m\angle ILM$ is about the relationship between $\angle KLM$ and $\angle ILM$, not related to $LH$ bisecting $\angle GLI$.
  • Option 3: If $m\angle GLI = 2m\angle GLH$, it means that $\angle GLH$ is half of $\angle GLI$. Since $\angle GLI=\angle GLH+\angle HLI$ and $m\angle GLI = 2m\angle GLH$, then $\angle GLH=\angle HLI$, so $LH$ is the bisector of $\angle GLI$.
  • Option 4: $m\angle GLI=\frac{1}{2}m\angle GLH+\frac{1}{2}m\angle HLI$ is incorrect. The correct relationship is $m\angle GLI=m\angle GLH + m\angle HLI$.

Answer:

$m\angle GLI = 2m\angle GLH$