Question

To construct a square, Dominic uses his straightedge to draw AB⎯⎯⎯⎯⎯ . He opens the compass to the length of AB⎯⎯⎯⎯⎯ and draws a circle centered at point A, and then, without changing the compass opening, draws a circle centered at point B. He marks the intersections of the circles as points C and D. What should Dominic do next? Change the compass opening to the length of CA⎯⎯⎯⎯⎯ and draw a circle centered at point C and then at point D. Change the compass opening to the length of CD⎯⎯⎯⎯⎯⎯ and draw a circle centered at point C. Use a straightedge to join points C and A, C and B, D and A, and D and B. Use a straightedge to join points C and D with a line.

Answer 1

Use a straightedge to join points C and A, C and B, D and A, and D and B. Use a straightedge to join points C and D with a line.

Explanation:

Given that Dominic uses his straightedge to draw AB⎯⎯⎯⎯⎯ .

He opens the compass to the length of AB⎯⎯⎯⎯⎯ and draws a circle centered at point A, and then, without changing the compass opening, draws a circle centered at point B.

He marks the intersections of the circles as points C and D.

Now we have AC=CB=BD=DA

Hence ACBE is a square

so next step is Use a straightedge to join points C and A, C and B, D and A, and D and B. Use a straightedge to join points C and D with a line.

Answer 2

Points C and D are equidistant from points A and B, so Dominic's square could be ACBD. To draw that square, his next move should be ...

... Use a straightedge to join points C and A, C and B, D and A, and D and B