What is the minimum number of straight lines that are needed to construct the…

Concept: When counting the minimum straight lines that build a composite figure, group every line by orientation — horizontal, vertical, or slanting — and count each line only ONCE per group. A single straight line stays one line even when other lines cross it partway or it passes through several marked points.

The figure may be labelled as shown, with points A to J marking the corners and crossings used to identify each line.

Application: Classify and count each orientation group in turn:

1. Horizontal lines: AE and JF each run the full horizontal extent of the figure, giving 2 horizontal lines.

2. Vertical lines: AJ, CH and EF each run the full vertical extent, giving 3 vertical lines.

3. Slanting lines — long diagonals: AG, BF, JD and IE each pass through one interior crossing point but remain single straight lines, giving 4 diagonals.

4. Slanting lines — outer triangle sides: AB, DE, JI and FG complete the slanting group, giving a further 4 lines, so slanting lines total 4 + 4 = 8.

5. Add the three orientation groups: 2 + 3 + 8.

Cross-check: Re-examine each of the 8 slanting lines individually to confirm it is genuinely one continuous straight line rather than two segments meeting at an angle — for instance, the points on diagonal AG lie on a single straight line through the interior crossing point, distinct from the BF diagonal. Since no segment is left uncounted and no line is split into two, the orientation-wise tally is confirmed.

So the minimum number of straight lines needed to construct the figure is 2 + 3 + 8 = 13.