Question

1. use the diagram to answer the following questions.

a) how many points appear in the figure? 9
b) how many lines appear in the figure? 13
c) how many planes appear in the figure? 5
d) name three collinear points. c, h, f
e) name four coplanar points. e, b, c, f
f) name the intersection of planes abc and abe. line ab
g) name the intersection of planes bch and def.
h) name the intersection of \\(\overline{ad}\\) and \\(\overline{df}\\).

Explanation:

Part g)

Step1: Recall plane intersection rule

Two planes intersect in a line. We analyze planes \( BCH \) and \( DEF \).

Step2: Identify common line

Planes \( BCH \) (containing points \( B, C, H \)) and \( DEF \) (containing \( D, E, F \)) intersect along line \( CF \) (or \( FH, CH \) but \( CF \) is the common line here as per the diagram's structure, assuming \( H \) is on \( CF \) extension and \( BCH \) plane connects to \( DEF \) via \( CF \)). Wait, actually, looking at the diagram (a 3D figure, maybe a prism or similar), planes \( BCH \) and \( DEF \) – let's re - examine. Wait, maybe the correct intersection is line \( CF \)? Wait, no, let's think again. Wait, the figure: points \( B, C, H \) (plane \( BCH \)) and \( D, E, F \) (plane \( DEF \)). The intersection should be a line. Looking at the diagram, \( CF \) is a line that is part of both? Wait, maybe \( EF \) is not, but \( CF \) – wait, maybe the correct answer is line \( CF \)? Wait, no, let's check the diagram again. Wait, the figure has \( B, C, H \) (with \( H \) on \( CF \)) and \( D, E, F \). So planes \( BCH \) and \( DEF \) intersect at line \( CF \) (since \( C \) and \( F \) are in both? Wait, \( C \) is in \( BCH \), \( F \) is in \( DEF \), and \( H \) is on \( CF \), \( E \) is inside. Wait, maybe the intersection is line \( CF \). Alternatively, maybe I made a mistake. Wait, another approach: two planes intersect in a line, so we need to find two points common to both planes. \( C \) is in \( BCH \) and \( F \) is in \( DEF \), and \( H \) is on \( CF \) (so \( H \) is in \( BCH \), \( F \) in \( DEF \)). Wait, maybe the intersection is line \( CF \) (or \( FH \), but \( CF \) is the segment between \( C \) and \( F \), with \( H \) on the extension). So the intersection of planes \( BCH \) and \( DEF \) is line \( CF \) (or \(\overleftrightarrow{CF}\)).

Part h)

Step1: Recall line intersection rule

Two lines intersect at a point. We have lines \(\overline{AD}\) and \(\overline{DF}\).

Step2: Find the common point

Line \(\overline{AD}\) goes from \( A \) to \( D \), and line \(\overline{DF}\) goes from \( D \) to \( F \). The common point of these two line segments is \( D \), since \( D \) is an endpoint of both \(\overline{AD}\) and \(\overline{DF}\).

g) Answer: \(\overleftrightarrow{CF}\) (or line \( CF \))

h) Answer: Point \( D \)

Answer:

Step1: Recall line intersection rule

Two lines intersect at a point. We have lines \(\overline{AD}\) and \(\overline{DF}\).

Step2: Find the common point

Line \(\overline{AD}\) goes from \( A \) to \( D \), and line \(\overline{DF}\) goes from \( D \) to \( F \). The common point of these two line segments is \( D \), since \( D \) is an endpoint of both \(\overline{AD}\) and \(\overline{DF}\).

g) Answer: \(\overleftrightarrow{CF}\) (or line \( CF \))

h) Answer: Point \( D \)