Name ________________________________________________ Date ___________ Basic Constructions Constructing Congruent Segments Example 1 Given: AB Construct: CD so that CD ≅ AB Step 1 Draw a ray with endpoint C. Step 2 Open the compass to the length of AB. Step 3 With the same compass setting, put the compass point on point C. Draw an arc that intersects the ray. Label the point of intersection D. (it helps here if you move the paper, not the compass) Practice: Use a straightedge to draw XY . Then construct RS so that RS = 2XY. Construct UV so that UV = AB + XY. Perpendicular Bisector: Example 2 Constructing the perpendicular bisector Given: AB Construct: XY so that XY ⊥ AB at the midpoint M of AB Step 1 Put the compass point on point A and draw a long arc. Step 2 With the same compass setting, put the compass point on point B and draw another long arc. Label the points where the two arcs intersect as X and Y. Step 3 Draw XY . The point of intersection AB and XY is M, the midpoint of AB . Practice: Construct EF so that it is half the length of AB .

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