Problem
Find every point the line passes through
A line is drawn across the surface of a triangular prism. We need to draw the same line on the prism's net.
Geometry
Your answer
How to solve
Strategy Visualize Spatial Relationships — A line drawn on a surface stays on whichever face it was on. So take it one face at a time: find the face each part of the line lies on, find that face in the net, and redraw the part between the same two points.
1STEP 1
Split the line by face
The line crosses two side faces: one part lies on face ABED and the other on face BCFE. Each part is a straight segment on its own face.
A → E, E → (midpoint of CF)
Two faces, two straight pieces.
7.G.A.3Draw A Diagram2STEP 2
Find those faces in the net
In the net the side faces lie in a row. The first rectangle is ABED and the one next to it is BCFE, with the shared edge BE between them.
ABED ∣ BCFE
Neighbouring faces stay neighbours.
6.G.A.4Identify SubproblemsFaces that touch on the solid still touch in the net.
Why?
A net is made by cutting some edges and folding the rest flat, so a face keeps its own shape and keeps every neighbour whose shared edge was not cut.
🧱Rigid motion preserves length and angleSliding, turning, or flipping a shape lays it exactly onto a copy, so every length and angle stays the same (folding is the flip case).
3STEP 3
Redraw the first piece
On the first rectangle, join A to E. Both are corners of that rectangle, so the segment is its diagonal.
A → E
The diagonal of the first rectangle.
7.G.A.3Visualize Spatial Relationships4STEP 4
Redraw the second piece
On the second rectangle, start again at E -- the same point where the first piece ended -- and go to the middle of the opposite upright edge CF.
E → (midpoint of CF)
The two pieces meet at E, just as on the solid.
7.G.A.3Visualize Spatial RelationshipsAnswer
On the net, draw the diagonal from A to E across the first side rectangle (face ABED), then from that same point E draw a segment across the next rectangle (face BCFE) to the midpoint of edge CF.
Fold it back in your head: the two segments meet at E on the shared edge, so the line joins up without a break, as it does on the solid.
Takeaway
A line on a solid stays on the face it was drawn on, so move it one face at a time.
- Split the line by face
- Find those faces in the net
- Redraw the first piece
- Redraw the second piece