CONSTRUCTING CONGRUENT LINE SEGMENTS

Transcription

1 NME: 1. Given: Task: Construct a segment congruent to. CONSTRUCTING CONGRUENT LINE SEGMENTS B a) Draw a new, longer segment with your straightedge. b) Place an endpoint on the left side of the new segment and label it '. c) Place the point of the compass on. d) Stretch the compass, so the pencil is exactly on B. e) Without changing the span of the compass, place the compass point on ' and swing an arc, so it crosses the segment you drew. f) The intersection of the segment and arc should be labeled B'. D 2. Given: CD Task: Construct a segment congruent to CD and label it C'D'. C Learning Constructions - Day 2 NME: CONSTRUCTING CONGRUENT LINE SEGMENTS 1. Given: Task: Construct a segment congruent to. B a) Draw a new, longer segment with your straightedge. b) Place an endpoint on the left side of the new segment and label it '. c) Place the point of the compass on. d) Stretch the compass so that the pencil is exactly on B. e) Without changing the span of the compass, place the compass point on ' and swing an arc, so it crosses the segment you drew. f) The intersection of the segment and arc should be labeled B'. D 2. Given: CD Task: Construct a segment congruent to CD and label it C'D'. C Learning Constructions - Day 2

2 NME: CONSTRUCTING CONGRUENT LINE SEGMENTS 1. Given: Task: Construct a segment congruent to. B D 2. Given: CD Task: Construct a segment congruent to CD, label it C'D'. Learning Constructions - Day 2 C NME: 1. CONSTRUCTING CONGRUENT LINE SEGMENTS Given: Task: Construct a segment congruent to. B D 2. Given: CD Task: Construct a segment congruent to CD, label it C'D'. C Learning Constructions - Day 2

3 NME: CONSTRUCTING PERPENDICULR BISECTOR 3. Given: Task: Bisect. B 4. Given: DE Task: Bisect DE and label the point of intersection as F. E D Learning Constructions - Day 2

4 NME: CONSTRUCTING PERPENDICULR BISECTOR 3. Given: Task: Bisect. a) Place your compass point on and stretch the compass MORE THN halfway to point B, but not beyond B. b) With this length, swing a large arc that will go BOTH above and below. c) Without changing the span on the compass, place the compass point on B and swing the arc again until the two arcs intersect both above and below B. d) With your straightedge, connect the two points of intersection. e) This new segment bisects. Label the point where the new segment and segment intersect as C. B 4. Given: DE Task: Bisect DE and label the point of intersection as F. E D Learning Constructions - Day 2

5 NME: CONSTRUCTING PERPENDICULR LINE FROM POINT ON LINE 5. Given: P is on line m. Task: Construct a line through P perpendicular to line m. P m Learning Constructions - Day 2

6 NME: CONSTRUCTING PERPENDICULR LINE FROM POINT ON LINE 5. Given: P is on line m. Task: Construct a line through P perpendicular to line m. a) Place your compass point on P and sweep an arc (below the line) of any size that crosses the line twice. You will be creating (at least) a semicircle. b) STRETCH THE COMPSS LRGER! c) Place the compass point where the arc crossed the line on one side and make a small arc below the line. (The small arc could be above the line if you prefer.) d) Without changing the span on the compass, place the compass point where the arc crossed the line on the OTHER side and make another arc. Your two small arcs should be crossing. e) With your straightedge, connect the intersection of the two small arcs to P. P m Learning Constructions - Day 2

7 NME: CONSTRUCTING PERPENDICULR LINE FROM POINT OFF LINE 6. Given: G is off a given line. Task: Construct a line through G perpendicular to the given line. G d Learning Constructions - Day 2

8 NME: CONSTRUCTING PERPENDICULR LINE FROM POINT OFF LINE 6. Given: G is off a given line. Task: Construct a line through G perpendicular to the given line. a) Place your compass point on Point G and sweep an arc of any size that crosses line d twice. b) Place the compass point where the arc crossed the line on one side and make an arc ON THE OPPOSITE SIDE OF LINE d. c) Without changing the span on the compass, place the compass point where the arc crossed the line on the OTHER side and make another arc. Your two new arcs should be crossing on the opposite sides of the line. d) With your straightedge, connect the intersection of the two new arcs to point G. G d Learning Constructions - Day 2

9 NME: 7. Given: P above line m. Task: Construct a line through P parallel to line m. CONSTRUCTING PRLLEL LINE FROM POINT OFF LINE P m Learning Constructions - Day 3

10 NME: CONSTRUCTING PRLLEL LINE FROM POINT OFF LINE 7. Given: P above line m. Task: Construct a line through P parallel to line m. a) Draw a point on line m to the left of P and label it Q. b) Place compass on Q and draw an arc through P that intersect line m. to the right of Q and label the intersection R. c) Using the same compass setting as the first arc, draw two more arcs: one from P, the other from R. d) Label the intersection of the two arcs S. e) Draw parallel to line m. P m Learning Constructions - Day 3

11 NME: CONSTRUCT PRLLEL SEGMENT THROUGH POINT ON SEGMENT 8. Given: B and C on BD. Task: Construct a line parallel to B through C. a) Copy B using C as the vertex of the new angle. B C D W 9. Given: XW and Y on XZ. Task: Construct a line parallel to XW through Y. X Y Z Learning Constructions - Day 3

12 NME: CONSTRUCT PRLLEL SEGMENT THROUGH POINT ON SEGMENT 8. Given: B and C on BD. Task: Construct a line parallel to B through C. B C D W 9. Given: XW and Y on XZ. Task: Construct a line parallel to XW through Y. X Y Z Learning Constructions - Day 3

13 NME: CONSTRUCTING CONGRUENT NGLES 10. Given: Task: Copy a) Using a straightedge, draw a ray. Label the left endpoint '. ith b) your Place straightedge. the compass point on vertex and swing an arc through both rays of. Mark the top intersection B and the lower C. c) Without changing the span of the compass, place the compass point on ' and swing the same arc. Mark the intersection C'. d) Place the compass point on B and open it to C. e) Without changing the span of the compass, place it on C' and swing an arc which intersects the first arc. Mark this B' f) Draw a ray from ' thru B'. 11. Given: F Task: Copy F F Learning Constructions - Day 4 NME: 10. Given: Task: Copy CONSTRUCTING CONGRUENT NGLES a) Using a straightedge, draw a ray. Label the left endpoint '. ith b) Place the compass point on vertex and swing an arc through both rays of. Mark the top intersection B and the lower C. c) Without changing the span of the compass, place the compass point on ' and swing the same arc. Mark the intersection C'. d) Place the compass point on B and open it to C. e) Without changing the span of the compass, place it on C' and swing an arc which intersects the first arc. Mark this B' f) Draw a ray from ' thru B'. 11. Given: F Task: Copy F F Learning Constructions - Day 4

14 NME: 10. Given: Task: Copy CONSTRUCTING CONGRUENT NGLES 11. Given: F Task: Copy F F Learning Constructions - Day 4 NME: CONSTRUCTING CONGRUENT NGLES 10. Given: Task Copy 11. Given: F Task: Copy F F Learning Constructions - Day 4

15 NME: CONSTRUCTING N NGLE BISECTOR 12. Given: Task: Bisect a) Place the point of the compass on vertex. b) Draw an arc which intersects both rays of. Mark the upper intersection B and the lower C. c) Place the compass point on B and swing an arc in the interior of the angle. d) Now, place the compass point on C and swing the same arc in the interior of the angle so that it intersects the first arc. e) Draw a line from vertex through the point where the arcs intersect in the angle's interior. Learning Constructions - Day 4 NME: CONSTRUCTING N NGLE BISECTOR 12. Given: Task: Bisect a) Place the point of the compass on vertex. b) Draw an arc which intersects both rays of. Mark the upper intersection B and the lower C. c) Place the compass point on B and swing an arc in the interior of the angle. d) Now, place the compass point on C and swing the same arc in the interior of the angle so that it intersects the first arc. e) Draw a line from vertex through the point where the arcs intersect in the angle's interior. Learning Constructions - Day 4

16 NME: CONSTRUCTING N NGLE BISECTOR 12. Given: Task: Bisect Learning Constructions - Day 4 NME: CONSTRUCTING N NGLE BISECTOR 12. Given: Task: Bisect Learning Constructions - Day 4

17 NME: 13. Given: Task: Divide CONSTRUCTING "n" CONGRUENT SEGMENTS into five congruent segments. B Learning Constructions - Day 5 NME: CONSTRUCTING N INSCRIBED EQUILTERL TRINGLE 14. Given: Circle F Task: Create an inscribed equilateral triangle. F Learning Constructions - Day 5

18 NME: 13. Given: Task: Divide CONSTRUCTING "n" CONGRUENT SEGMENTS into five congruent segments. a) Opening at an upward acute angle, draw a long segment from endpoint. b) Set the compass at a narrow opening so "n" [5 for this example] segments can be created. Mark and label the points C, D, E, F & G. c) Opening at a downward acute angle, draw a long segment from endpoint B. Use the same compass setting to mark "n" segments [5 on this line]. d) Label the points created H, I, J, K & L. e) Connect the "n" arc markings on the segments above and below the original line: G to B, F to H, E to I, D to J, C to K, and to L. There will be "n" congruent segments created by the connecting lines intersecting the original line. B Learning Constructions - Day 5 NME: CONSTRUCTING N INSCRIBED EQUILTERL TRINGLE 14. Given: Circle F Task: Create an inscribed equilateral triangle. a) Set a compass to the length of the circle F radius. b) Using the intersection of the diameter and the circle, create a new circle with the same radius. c) The two circles will interesect at two points. Set your compass to distance between these two points. d) e) With the compass point on one of the points of intersection, swing a small arc to mark a new intersection to circle F. Connect the three intersections of circle F to form an equilateral triangle. F Learning Constructions - Day 5

19 NME: CONSTRUCTING N INSCRIBED REGULR HEXGON 15. Given: Circle G Task: Create an inscribed regular hexagon. G Learning Constructions - Day 5 NME: CONSTRUCTING N INSCRIBED REGULR PENTGON 16. Given: Circle J Task: Create an inscribed regular pentagon. J Learning Constructions - Day 5

20 NME: CONSTRUCTING N INSCRIBED REGULR HEXGON 15. Given: Circle G Task: Create an inscribed regular hexagon. a) Set a compass to the length of the radius of circle G. This will be the length of each side of the hexagon. b) Using this setting, place your compass on the left intersection of the circle and its diameter and swing two intersecting arcs, one above and one below the circle's diameter. c) Repeat step "b)" with your compass point on the right intersection of the circle and its diameter. d) Connect the six points. G Learning Constructions - Day 5 NME: 16. CONSTRUCTING N INSCRIBED REGULR PENTGON Given: Circle J Task: Create an inscribed regular pentagon. a) Draw a diameter of the circle through the center point and mark its endpoints C and M. [Note: It does not have to be vertical.] b) Construct a ray perpendicular to CM at point O. c) Mark the point S where it crosses the circle. d) Find the midpoint of SO by constructing its perpendicular bisector. Label the midpoint L. e) Set the compass on L, adjust its width to S or O and draw a circle. f) Draw a line from M through L, so it crosses the small circle in two places. Label the closer to M intersection P and further N. g) Set the compass on M and adjust its width to P. h) Draw a broad arc that crosses the given circle in two places. Label them and E. i) Set the compass on M and adjust its width to N. j) Draw a broad arc that crosses the given circle in two places. Label the points B and D. k) Draw a line from to B, then B to C, etc. until you have drawn all five sides of the pentagon. O Learning Constructions - Day 5