Question

signs in the figure, $overrightarrow{dg}$ and $overrightarrow{dp}$ are in plane $j$ and $h$ lies on $overrightarrow{dg}$. state the postulate that can be used to show that each statement is true. 3. points $g$ and $p$ are collinear. 4. points $d$, $h$, and $p$ are coplanar.

Explanation:

Step1: Analyze collinearity

Collinear points lie on the same line. Since $\overrightarrow{DG}$ and $\overrightarrow{DP}$ are in plane $J$, and there is no information suggesting that $G$ and $P$ are on the same line, this statement is false. There is no postulate to support it.

Step2: Analyze coplanarity

Coplanar points lie in the same plane. $\overrightarrow{DG}$ and $\overrightarrow{DP}$ are in plane $J$, and $H$ lies on $\overrightarrow{DG}$. So, points $D$, $H$, and $P$ are in plane $J$. The postulate that can be used is: If two lines (in this case, parts of $\overrightarrow{DG}$ and $\overrightarrow{DP}$) are in a plane, then the points on those lines are coplanar.

Answer:

1. There is no postulate as the statement is false.
2. If two lines are in a plane, then the points on those lines are coplanar.