Geometry 3.02: Constructions of Segments, Angles, and Bisectors

Mayumi is constructing a line through point P that is perpendicular to RS←→. She places her compass on point P to construct an arc.

It must be wide enough so that the arc intersects RS←→ in two points.

What are the steps for using a compass and straightedge to construct the bisector of ∠A? Drag the steps and drop them in order from start to finish.

Place the point of the compass on point A and draw an arc that intersects the sides of ∠A. Label the points of intersection as points B and C. Place the point of the compass on point B and draw an arc in the interior of the angle. Without changing the opening of the compass, place the point of the compass on point C and draw another arc in the interior of the angle. Label the intersection of the arcs in the interior of the angle as point D. Use the straightedge to draw AD→.

Ashton is constructing the bisector of MN¯¯¯¯¯¯¯. What should Ashton do for his first step?

Place the point of the compass on point M and draw an arc, making sure the width of the compass opening is greater than 1/2 MN.

Nadine is constructing a line perpendicular to KE←→ . She has constructed the arcs as shown. What is the next step in her construction?

Use a straight edge to draw a line through D and M.

Joel is constructing a line perpendicular to BW←→− . He has already constructed three arcs as shown. He moves his compass point to W to construct a fourth arc. What must be true about the width of Joel's compass opening before he draws the arc?

It must be the same as it was when constructing the arc above P.

Natasha is constructing the bisector of PQ¯¯¯¯¯. She has already constructed an arc as shown. What should Natasha do for her next step?

Place the point of the compass on point Q and draw an arc, using the same width for the opening of the compass as the first arc.

What are the steps for using a compass and straightedge to construct the bisector of ∠R? Drag the steps and drop them in order from start to finish.

Place the point of the compass on point R and draw an arc that intersects the sides of ∠R. Label the points of the intersection as points S and T. Place the point of the compass on point S and draw an arc in the interior of the angle. Without changing the opening of the compass, place the point of the compass on point T and draw another arc in the interior of the angle. Label the intersection of the arcs in the interior of the angle as point U. Use the straightedge to draw RU→.

What are the steps for using a compass and straightedge to construct a line through point X that is parallel to line r? Drag the steps and drop them in order from start to finish.

Use the straightedge to draw a line s that passes through X and intersects line r. Label the point of intersection as point Y. Place the point of the compass on point Y and draw an arc that intersects lines r and s. Label the intersections as points M and N. Without changing the width of the compass opening, place the point of the compass on point X and draw an arc that intersects line s. Label the intersection as point P. Place the point of the compass on point M and open it to width MN. With the compass opening set to width MN, place the point of the compass on point P and draw an arc that intersects the arc that was drawn from point X. Label the intersection of the arcs as point Z. Use the straightedge to draw XZ←→.

What are the steps for using a compass and straightedge to construct a line through point A that is parallel to line j? Drag the steps and drop them in order from start to finish.

Use the straightedge to draw line k that passes through A and intersects line j. Label the point of intersection as point P. Place the point of compass on point P and draw an arc that intersects lines j and k. Label the intersections as points Q and R. Without changing the width of the compass opening, place the point of the compass on point A and draw an arc that intersects line k. Label the intersection as point S. Place the point of that compass on point Q and open it to width QR. With the compass opening set to width QR, place the point of the compass on point S and draw an arc that intersects the arc that was drawn from point A. Label the intersection of the arcs as point B. Use the straightedge to draw AB←→.

Ricardo is constructing a line through point P that is perpendicular to line m. He has already constructed the arc shown. He places his compass on point X to construct an arc. What must be true about the width of the compass opening when Ricardo draws the arc?

It must be greater than 1/2 XY.