Question

standard: g.gsr.4.1 - dok2
\\(\overleftrightarrow{ab}\\) and \\(\overleftrightarrow{cd}\\) intersect at point (z).
which statement is true about the points?
points a, b, c, d, and z are all in the same plane because there are 3 points on the same line.
points a, b, c, d, and z are all not in the same plane because there are 3 points on the same line.
points a, b, c, d, and z are all in the same plane because there are 3 points on the same line.
points a, b, c, d, and z are all in the same plane because any 3 points on the same line.
points a, b, c, d, and z are all not in the same plane because any 3 points not on the same line.

Explanation:

Step1: Recall plane - point relationship

Any two intersecting lines lie in the same plane. Since $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ intersect at point $Z$, points $A$, $B$, $C$, $D$, and $Z$ which lie on these two intersecting lines are all in the same plane. Also, any three points on the same line (collinear points) can be used to determine a plane. In the case of two intersecting lines, we can use the fact that we can consider points on each line and the intersection point.

Answer:

Points A, B, C, D, and Z are all in the same plane because there are 3 points on the same line.