Geometry Foundations Exam Part One

The big idea Review the compass-and-straightedge constructions that can appear on the Geometry Foundations test.

Copy a segment

Draw a new ray. Open the compass to the full length of the given segment. Do not change the width. Put the compass point on the new ray’s endpoint and swing an arc across the ray. The endpoint and arc intersection form the copied segment.

Construction clue: one fixed compass opening transfers one length.

A compass transferring a segment length to a new ray — The compass carries the original segment length to the new ray.

Copy an angle

Draw a new ray. From the original vertex, draw an arc crossing both sides of the angle. Keep that radius and draw the same arc from the new vertex. Then copy the distance between the original arc’s two crossing points onto the new arc. Draw the second ray through the new intersection.

Remember: first copy the arc radius; then copy the chord between the two arc hits.

A copied-angle construction with matching arcs and a transferred chord — The copied chord creates the same angle opening.

Bisect a segment or angle

Segment: use one compass width—more than half the segment—from both endpoints. The arcs cross above and below. Draw the line through those crossings.

Angle: draw one arc from the vertex that hits both rays. From those two hits, draw equal interior arcs. Draw a ray from the vertex through their intersection.

A segment bisector made with paired intersecting arcs — Equal arcs from both endpoints locate the segment bisector.

An angle bisector made with equal intersecting arcs — The ray through the interior arc crossing divides the angle equally.

Parallel, perpendicular, and inscribed figures

To construct a parallel line through a point, draw a transversal and copy the corresponding angle at the new point. To construct a perpendicular line, use equal arcs to locate a line that meets the original at 90°.

For an inscribed triangle, step the circle’s radius around the circle and connect every other mark. For a square, construct perpendicular diameters and connect their four endpoints. For a hexagon, connect all six neighboring radius-width marks.

A parallel line made by copying a corresponding angle — Equal corresponding angles create parallel lines.

A triangle, square, and hexagon inscribed in circles — Each regular figure uses equally spaced points on the circle.

Check Part 2

Use the construction order—not how the finished picture looks—to choose each answer.

1 / 4 0 correct