Copy any angle exactly using SSS congruence, and use that to construct a line parallel to a given line.
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Repeating a design unit needs identical angles, not just equal arms.
In Fig. 6.6 one unit repeats itself, in two different orientations.
Five steps from the book.
Problem. Draw an angle at A. Make an exact copy of it at X, using only a ruler and compass. (Textbook pp. 146–147)
Practise copying and use it for the repeating fan design.
Figure it Out, Textbook p. 147, Q1–Q2.
How did you make every unit's angle and arms the same?
Copy the corresponding angle at B and the new line is parallel.
Lines are parallel when they make equal corresponding angles with a transversal. Earlier we used a set square for this.
The book's Figs. 6.7–6.10, step by step.
Problem. Construct a line through B parallel to m. (Textbook pp. 147–148)
The figure for the next task.
Figure it Out, Textbook p. 148, Q2. The figure to construct:
Construct parallel pairs and the book's 8-pointed star.
Figure it Out, Textbook p. 148, Q1–Q2.
Which angle did you copy?
Look for lines through the centre and angles between them.