Question

2025 geometry fall measuring length and angles raj correctly determined that ray lh is the bisector of ∠gli. which information could he have used to determine this? ∠glh≅∠ilm m∠gli = 2m∠glh m∠klm = 5m∠ilm m∠gli = 1/2m∠glh

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

Step2: Analyze each option

• Option $\angle GLH\cong\angle ILM$ has no relation to $\angle GLI$ being bisected by $LH$.
• Option $m\angle GLI = 2m\angle GLH$ means that $\angle GLH$ and $\angle HLI$ are equal since $m\angle GLI=m\angle GLH + m\angle HLI$ and if $m\angle GLI = 2m\angle GLH$, then $m\angle GLH=m\angle HLI$. This is consistent with the definition of an angle - bisector.
• Option $m\angle KLM = 5m\angle ILM$ has no relation to $\angle GLI$ being bisected by $LH$.
• Option $m\angle GLI=\frac{1}{2}m\angle GLH$ is incorrect as it should be $m\angle GLI = 2m\angle GLH$ for $LH$ to be the bisector of $\angle GLI$.

Answer:

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