CONSTRUCTION SOL PROBLEMS

Transcription

1 Modified and Animated By Chris Headlee Dec 2011 CONSTRUCTION SOL PROBLEMS Super Second-grader Methods SOL Problems; not Dynamic Variable Problems

2 Use scratch paper to measure AB See which line segment cuts AB in half Draw the connecting line segments with your ruler See which one appears to cut AB in half

3 Use straight-edge tool to continue lines as far as possible Eliminate W and Z Compare distance between PY and YR Compare distance between PX and RX Angle bisector: 1) draw equal distance points (arc tool) from Q 2) draw equal distance arcs from those two points 3) connect Q and two arc intersection point 4) Point Y is on the line (angle bisector)

4 Use scratch paper to measure BC Measure out from P Use arc tool to set BC distance Move tool to P and see that point R is answer

5 Equal Distances from the endpoints M and N: Isosceles triangle formed Altitude bisects MN Connect the x s See what s drawn

6 Use ruler if available Use scratch paper as ruler double each answer and see which one is the same length as PQ

7 Our eyes tell us that ABD and DBC are equal Construction is an angle bisector ABC is the whole and ABD and CBD are the halves

8 use edge of scrap paper to estimate perpendicular line Draw arc from Z intersecting line l twice From intersecting points draw arcs (same distance) below line l Connect point Z and intersecting point below line l Line passes closest to W

9 something to do with an angle eliminates H and J The construction divides the given angle in half

10 Use ruler or scratch paper to measure AB Compare to all other segments Draw an arc with center at A and passes through B Which ever point the arc passes through is equal distant

11 use scratch paper to measure AB See which point gives same distance Use compass to measure AB Place at C and see where it hits

12 Use scratch paper lines and edge to match A with X Use compass to find two points on line l equal distant from A Draw two arcs (with same radius) from those points Connect their intersection and point A

13 Use scratch to measure distance from end of arcs to each point The point that is equidistant is the answer Use compass to find two points on rays equal distant from C Draw two arcs (with same radius) from those points Connect their intersection and point C

14 not much help arc #1 gives a pair of points equal distant from the drawn point; then arcs 2, 3, and 4 are drawn from those first points

15 use scrap paper to measure AB reposition on AQ put compass end at A and the pencil end at B draw an arc that crosses AQ

16 Use scrap paper to align line with AB and see what lines up with P Put compass at P and draw an arc crossing AB From those intersection points draw an arc below the line from each intersection Connect P to the intersection (going through W)

17 no right angles no perpendiculars Angle bisector problem

18 Use scrap paper to line up lines and points Draw two arcs on line that are equidistant from T From those points draw an arc above T Draw a line from the intersection of those two arcs and point T

19 use scarp paper to line up corner with point A Point X is the perpendicular

20 look at picture Q and T have to be wrong measure AB; fold paper in half see which point lines up draw an arc above and below AB from A draw an arc above and below AB from B connect intersections and see they go through S

21 Use scratch paper to measure two points on edges that are equidistant from Q The answer point that is equidistant from them is the answer Use compass to find two points on rays equal distant from Q Draw two arcs (with same radius) from those points Connect their intersection and point Q

22 must be with angles two separate angles copy an angle drawing an angle congruent to another

23 use corner of scrap paper to line up X is answer make a point toward S that is same distance as T is from O using that new point draw arcs above and below line go back to T and draw arcs (of same distance) above and below the line line through intersections goes through X

24 copy angle fold in half see which point it goes through make two points equal distance from vertex on angle sides using one new point draw arc between edges using other new point draw arc (of same length) between edges line through intersection and vertex goes through S

25 measure AB with scrap paper see which point lines up answer is B using compass: set end at A and set an arc of length AB drag compass to C keeping length the same draw and arc and see it pass through point E

26 use corner of scrap paper to line up Q is answer make a point toward B that is same distance as A is from P using that new point draw arcs above and below line go back to A and draw arcs (of same distance) above and below the line line through intersections goes through Q

27 use scrap paper to line up G is answer draw arcs above and below line from B go back to A and draw arcs (of same distance) above and below the line line through intersections goes through X and Z

28 copy angle fold in half see which point it goes through make two points equal distance from vertex on angle sides using one new point draw arc between edges using other new point draw arc (of same length) between edges line through intersection and vertex goes through K

29 must involve perpendicular eliminates A need two arcs crossing line equidistant from point need an arc from each of those intersection points on the other side of the line

30 use corner of scrap paper to line up X is answer make two points equal distance from K using those new points draw an arcs to the left of the line line through intersection and K goes through X

31 copy angle fold in half see which point it goes through make two points equal distance from vertex on angle sides using one new point draw arc between edges using other new point draw arc (of same length) between edges line through intersection and vertex goes through X

32 use edge of scrap paper to estimate perpendicular line Draw arc from O intersecting line ST twice From intersecting points draw arcs (same distance) to left of ST Connect point O and intersecting point to the left Line passes closest to W

33 use scrap paper to check QR and RS (they are different!!) make point T so that RT = RQ measure distances from Q to and answer and from T which one is equal is correct Use compass to find two points on rays equal distant from R note: Q and S are not! Draw two arcs (with same radius) from those points Connect their intersection and point R

34 something to do with an angle two of them two congruent angles