Question

geometry part 2 ai teacher (acc ed) / trigonometric ratios

• $overline{gi}$ is an altitude of $\triangle gji$
• $overline{gj}$ is an altitude of $\triangle gjh$
• $overline{ji}$ is an altitude of $\triangle hji$
• $overline{jh}$ is an altitude of $\triangle gji$

Explanation:

Step1: Recall Altitude Definition

An altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side.

Step2: Analyze Each Option

• Option 1: $\overline{GI}$ – Check if it's perpendicular to the opposite side in $\triangle GJI$. From the diagram, it doesn't appear perpendicular.
• Option 2: $\overline{GJ}$ – In $\triangle GJH$, $\angle GJH$ is a right angle, so $\overline{GJ}$ is perpendicular to $\overline{JH}$ (the opposite side of vertex $G$ in $\triangle GJH$). This fits the altitude definition.
• Option 3: $\overline{JI}$ – In $\triangle HJI$, check perpendicularity. The diagram doesn't show $\overline{JI}$ as perpendicular to the opposite side.
• Option 4: $\overline{JH}$ – In $\triangle GJI$, $\overline{JH}$ is not perpendicular to the opposite side (visually, it's part of the right angle at $J$ but not the altitude for $\triangle GJI$).

Answer:

$\boldsymbol{\overline{GJ}}$ is an altitude of $\boldsymbol{\triangle GJH}$ (the option with $\overline{GJ}$ is an altitude of $\triangle GJH$)