Question

3 from unit 1, lesson 2 starting with two marked points, a and b, precisely describe the straightedge and compass moves required to construct the triangle abc in this diagram.

Explanation:

Step1: Set the compass width to \(AB\)

Open the compass so that the distance between the compass - point and the pencil is equal to the length of segment \(AB\).

Step2: Draw a circle centered at \(A\)

With the compass set to the width of \(AB\), place the compass - point at \(A\) and draw a circle.

Step3: Draw a circle centered at \(B\)

Without changing the compass width (still set to \(AB\)), place the compass - point at \(B\) and draw a second circle.

Step4: Mark the intersection point \(C\)

The two circles intersect at two points. Mark one of the intersection points as \(C\).

Step5: Connect the points

Use a straightedge to connect \(A\) to \(C\) and \(B\) to \(C\) to form triangle \(ABC\).

Answer:

1. Set the compass width to \(AB\). 2. Draw a circle centered at \(A\). 3. Draw a circle centered at \(B\) (same compass width). 4. Mark an intersection point of the two circles as \(C\). 5. Use a straightedge to connect \(A - C\) and \(B - C\) to form \(\triangle ABC\).