Common Core State Standards High School Geometry Constructions
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1 ommon ore State Standards High School Geometry onstructions HSG.O..12 onstruction: opying a line segment HSG.O..12 onstruction: opying an angle HSG.O..12 onstruction: isecting a line segment HSG.O..12 onstruction: isecting an angle HSG.O..12 onstruction: line perpendicular to a given line through a given point on the line HSG.O..12 onstruction: line perpendicular to a given line through a given point not on the line HSG.O..12 onstruction: perpendicular bisector of a line segment HSG.O..12 onstruction: line parallel to a given line through a given point not on the line HSG.O..13 onstruction: n equilateral triangle inscribed in a circle HSG.O..13 onstruction: square inscribed in a circle HSG.O..13 onstruction: regular hexagon inscribed in a circle HSG...3 onstruction: The inscribed circle of a triangle HSG...3 onstruction: The circumscribed circle of a triangle HSG...4 onstruction: tangent line from a point outside a given circle to the circle eveloped through the PIS Project ( with funding from the National Science oundation.
2 HSG.O..12 onstruction: opying a line segment Given: 1. Start by labeling point not on. 2. Place the point of the compass on point. onstruct an arc that passes through point. Without changing the angle of the compass, move the point of the compass to point and construct an arc. 3. Use a straight edge to draw a straight line segment from point to any point on the arc just drawn. Label this point. The line segment will be congruent to. eveloped through the PIS Project ( with funding from the National Science oundation.
3 HSG.O..12 onstruction: opying an angle Given: 1. Start by drawing separate from with your straight edge. G 2. Place the point of the compass on point and set its width so that an arc can be constructed to cross. xtend the arc to cross both and. Label the points of intersection and G. G 3. Without changing the width of the compass, set the point of the compass on point and construct an arc that crosses. Label the intersection point I. I eveloped through the PIS Project ( with funding from the National Science oundation.
4 G H I 4. Set the point of the compass on point G and extend the compass to point and construct an arc. Without changing the width of the compass, set the point of the compass on point I and construct an arc across the existing arc. Label point of intersection H. 5. raw a ray starting at point through point H. HI is congruent to. H G I eveloped through the PIS Project ( with funding from the National Science oundation.
5 HSG.O..12 onstruction: isecting a line segment MO VRSION Given: 1. Set the point of the compass on point and set the width of the compass so that it is at least half that of but not as far out as point. onstruct an arc above and an arc below. MO VRSION 2. Now set the point of the compass on point and the marking end more than half the distance of. onstruct two more arcs, once again above and below. Label the intersection points and. MO VRSION 3. Using a straight edge, connect points and. is the midpoint of and any line through bisects. eveloped through the PIS Project ( with funding from the National Science oundation.
6 HSG.O..12 onstruction: isecting an angle Given: 1. Place the point of the compass on point. Set the width of the compass so that it lies on. Without changing the width of the compass, construct an arc crossing and. Label the intersection points and. 2. Without changing the width of the compass, set the point of the compass on point and draw an arc between and. 3. Without changing the width of the compass, set the point of the compass on point and construct an arc between and. This arc should intersect the one made in the previous step. Label the intersection point. 4. raw a ray starting at point through point. This ray bisects. eveloped through the PIS Project ( with funding from the National Science oundation.
7 HSG.O..12 onstruction: line perpendicular to a given line through a given point on the line Given: Point on XY X Y 1. Start with the point of the compass on point of XY. Set the compass to a short width and, without changing the width of the compass, construct two arcs intersecting XY, one on each side of point. Label the points of intersection and. X X Y Y 2. Set the point of the compass on point and construct an arc above point. 3. Without changing the width of the compass, set the point of the compass on point and construct an arc which intersects the arc from the previous step. Label the point of intersection. 4. raw a line through and. XY and are perpendicular. X Y eveloped through the PIS Project ( with funding from the National Science oundation.
8 HSG.O..12 onstruction: line perpendicular to a given line through a given point not on the line Given: Point not on XY X Y 1. Place the point of the compass on point and set the width to any point on XY. onstruct two arcs intersecting XY, one on either side of point. Label the points of intersection and. X Y 2. Without changing the angle of the compass, set the point of the compass on point and construct an arc below XY that passes under point. X Y 3. Without changing the angle of the compass, set the point of the compass on point and construct an arc below XY that intersects the arc from the previous step. Label the point of intersection. 4. raw a line through and. is perpendicular to XY. X Y eveloped through the PIS Project ( with funding from the National Science oundation.
9 HSG.O..12 onstruction: perpendicular bisector of a line segment MO VRSION Given: 1. Set the point of the compass on point and set the width of the compass to at least half that of. onstruct an arc above and an arc below. MO VRSION 2. Now set the point of the compass on point and the marking end more than half the distance of. onstruct two more arcs, once again above and below. Label the intersection points and. MO VRSION 3. Using a straight edge, connect points and. is the midpoint of and is the perpendicular bisector of. eveloped through the PIS Project ( with funding from the National Science oundation.
10 HSG.O..12 onstruction: line parallel to a given line through a point not on a line 1. Given: Point not on 2. raw a line through and. Label the point where the two lines intersect. 3. Place the point of the compass at point and set its width to be between points and. onstruct an arc using this width. eveloped through the PIS Project ( with funding from the National Science oundation.
11 G 4. Without changing the width of the compass, place the compass point on point and construct another arc. Label the points of intersection,, and G. 5. Set the compass point on point and set the width to point and draw an arc. Without changing the width of the compass, set the compass point on point G and construct an arc intersecting the arc that passes through G. Label the point of intersection H. 6. Using a straight edge, draw a line through and H. This line is parallel to. eveloped through the PIS Project ( with funding from the National Science oundation.
12 HSG.O..13 onstruction: n equilateral triangle inscribed in a circle Given: ircle with center. 1. Select any point on the circle. raw the diameter of the circle by using a straight edge to draw a line segment from point through point to the opposite side of the circle. Label the second point on the circle point. 2. Place the point of the compass on point. Set the width to point. onstruct a semicircle through and two other points on the circle. Label these points and. 3. Use your straight edge to connect points,, and. eveloped through the PIS Project ( with funding from the National Science oundation.
13 HSG.O..13 onstruction: square inscribed in a circle Given: ircle with center Z Z 1. Use your straight edge to draw a diameter of the circle. Name the points where the diameter intersects the circle points and. Z 2. onstruct the perpendicular bisector of (see HSG.O..12 onstruction: Perpendicular bisector of a line segment). Where the perpendicular bisector intersects the circle, label points and. 3. Use your straight edge to draw,,, and. Z eveloped through the PIS Project ( with funding from the National Science oundation.
14 HSG.O..13 onstruction: regular hexagon inscribed in a circle Given: ircle with center 1. Label any point on the circumference of the circle point. 2. Set the point of your compass on point set the width to point and make an arc. Without changing the width of the compass, construct an arc across the circumference of the circle. Where the arc intersects the circle, label point. G G 3. Without changing the width of the compass, place the point of the compass on point and construct a new arc across the circumference of the circle. Where the new arc meets the circle, label the point of intersection. Repeat this step, moving the point of the compass to each new point and naming the points as they are created, until you have six points on the outside of your circle. 4. raw line segments connecting each point on the circle to the next point until you have a hexagon. eveloped through the PIS Project ( with funding from the National Science oundation.
15 HSG...3 onstruction: The inscribed circle of a triangle Given: 1. onstruct the angle bisector of. Refer back to directions on bisecting an angle if needed: HSG.O..12 onstruction: isecting an angle 2. onstruct the angle bisector of. Label point where the two angle bisectors meet. 3. onstruct the angle bisector of (it should also go through point ). Point is the incenter. 4. onstruct a line perpendicular to through point (see HSG.O..12 onstruction: onstructing a perpendicular line from a point not on a line if needed). Where this line meets, label point. 5. Place the point of the compass on point and set the width to point. onstruct a circle with radius. eveloped through the PIS Project ( with funding from the National Science oundation.
16 HSG...3 onstruction: The circumscribed circle of a triangle Given: 1. onstruct the perpendicular bisector of (see HSG.O..12 onstruction: Perpendicular bisector of a line segment if needed). 2. onstruct the perpendicular bisector of. 3. onstruct the perpendicular bisector of the third side,. Where the perpendicular bisectors meet, label point. Point is the circumcenter. 4. Place the point of the compass on point. Set the width to any vertex of the triangle. onstruct a circle using this width. eveloped through the PIS Project ( with funding from the National Science oundation.
17 HSG...4 onstruction: tangent line from a point outside a given circle to the circle 1. onstruct circle O and a point P outside of the circle. 2. raw a line segment from O to P using a straight edge. 3. onstruct the perpendicular bisector of OP (see HSG.O..12 onstruction: Perpendicular bisector of a line segment if needed) to find the midpoint of OP. 4. reate points J and K by placing the compass on the midpoint of OP, setting its width to O and drawing the two possible arcs across the circle. 5. Use a straight edge to connect J and P and then K and P. JP and KP are tangent to the circle and pass through P. eveloped through the PIS Project ( with funding from the National Science oundation.
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