## Tuesday, 27 June 2017

### Geometrical Construction: Spot the Error (1)

As a group, watch the clip and try to spot as many errors as possible.

1. He did not extend the compass all the way to point B. And he drew the arcs from Point A and C, rather than Point B.

1. What assumption did he have when he drew the arcs from points A and C?
Why did you suggest extend the compass all the way to point B?

2. He should made the distance between the compass's point and pencil the distance of CB

1. I could not quite make out what you try to describe.
Are you trying to say that he should place the pointed end of the compass at point B?
Then, what's next?

3. The compass did not reach Point B.

1. Are you suggesting that the pointed end of the compass should be placed at point A and C, but each time to stretch the arm to touch point B?
Watch the clip (in the GoogleSite) on how to construct angle bisector again and compare.

4. When drawing the arc, he did not extend the compass to point B.

1. Before stretching the compass to point B, check - did he place the sharp end of the compass at the correct place?

5. he drew the longer diagonal inclined to line BC, not through the vertex.

1. As this is not an enclosed figure (4 sides or more), there is no diagonal.
What do you mean when you say, he drew the longer diagonal "inclined" to line BC?

6. The compass should stretch out from point A to B but he did not extend the compass to point B.

1. Check again, did he place the pointed end of the compass at the correct place (to start the construction)? OR is there some assumption he made to the lengths of AB and BC?

7. The compass should draw the arc first and use each point of the arc to draw another arc

1. You are right to some extent... however, you need to be more specific.
Where should he place the pointed end of the compass at to draw the arc first?
(this step is critical)

8. He did not stretch the arm of the compass to point B when drawing the arc

1. Check again!
Before he start 'stretching' the arm of the compass, has he placed the pointed end of the compass at the correct place?

9. He did not make the compass extend all the way to point B.

1. Check again!
Before he start 'extending' the arm of the compass, has he placed the pointed end of the compass at the correct place?

10. He did not stretch the compass to the vertex (B)

1. Check again!
Before he start 'stretching' the arm of the compass to B, has he placed the pointed end of the compass at the correct place?

11. The angular bisector was exactly connecting to point ABC

1. You have not described what was not correctly done yet.

12. He did not extend the legs of the compass more so that it will be as long as AB and BC.

1. You are right to point out (indirectly) that the length of AB and BC need to be looked into. However, you need to be more precise. So, what was not correctly done (from the video)?

13. The bisector did not reach the vertex.

1. Before talking about the bisector, what was incorrect in the way he did the construction?

14. He did not draw the arcs

1. You are right to some extent, however need to be more precise.
How should he draw the arcs?
You also need to point out what's wrong with the method you saw in the video clip.

15. It is because that he did not not extend the compass arm so that it is long enough so that point a can touvh point b.

1. Before talking about extending the compass, examine where he has placed the pointed-end of the compass, did you notice something not quite right?
Watch the clip to see the difference: https://sites.google.com/a/s2017.sst.edu.sg/math/sdl-03-geometrical-construction/2-angle-bisector

16. 1) His angle bisector is not accurate as he did not draw the bisector across the vertex but across the arms.
2) He should have marked a line at the middle of both arms BC and BA, then continuing from that marked line, he should draw the arcs from line, and then draw the bisector through the intersecting points of both arcs and the vertex.

1. You have correctly pointed out that the issue lies on where thy place compass. The pointed-end should be placed at the vertex.

Point 2 could be clearer.
Before marking "a line at the middle of both arms BC and BA", indicate where he should place the pointed end of the compass (i.e. point B), then mark the "arcs" so that .... (then you continue to explain). The above sentence is important because is shows how one could mark points along BC and BA such that the distance between the arc and the B from both arms are the same (before any further drawing takes place).

17. The straight line was not drawn accurately to separate the vertex in half equally. We have to mark a arcs on lines AB and BC before drawing the bisector.

1. The first sentence is not quite clear.
The "straight line" you mentioned - are you referring to the "angle bisector" drawn?
(Then you would need to apply the vocabulary).

The 2nd sentence has clearly pointed out the important step that was missed out. Good.
You could actually describe further to give a complete description on how to construct the angle bisector :)

18. 1. He should have first drawn two arcs by putting the Compass Point at point B.
2. He should then have put the Compass Point on the intersection of the arc and line AB and then draw an arc, and do likewise for line BC.

1. Very clear description on how he should have placed the compass at the various points for the drawing.

On another note, do you know the assumption he made when starting by placing the pointed end at points A and C?

19. The bisector was not accurate as it was not drawn across the vertex.
He should have drawn from the middle points of BA and BC which should have done earlier, and then draw arcs to draw the angle bisector.

1. Could be clearer to describe what you mean by "not drawn across the vertex".
Are you trying to say that an important step is missing?

Why do you think he could have drawn from teh middle points of BA and BC?
Watch the video clip and examine where are the correct places to place the pointed end of the compass before drawing the 'arcs': https://sites.google.com/a/s2017.sst.edu.sg/math/sdl-03-geometrical-construction/2-angle-bisector

20. Firstly, he should have placed the pointed end of the compass at point B.
From what we have learnt, he should have marked out 2 arcs on the lines CB and AB. He should also make sure that the length of the compass used to mark out the 2 arcs is the same.
From there, he should place the sharp ends of the compass on the point where the lines CB and AB intersects the 2 arcs and draw another 2 arcs.
Finally, he should draw the bisector through the intersecting points of both arcs and the bisector should reach point B.

1. Very clear description on how to construct the angle bisector. Good.

On another note, do you know what assumption (in the video) was made when points A and C are used?

21. Firstly, he should have placed the Compass Point on point B and drawn 2 arcs on the 2 lines, AB and BC, instead of drawing 2 arcs from the points A and C. Next, he should put the Compass Point on the point which intercepts the line AB and draw 2 arcs. He should do the same for the line BC. Lastly, he should draw a bisector which cuts through point B and the intersection points of the arcs.

1. Very clear explanation. Good.

Note: line 2 - "... point which intercepts the line...." - use "intersect" instead of "intercept"

22. He should have drawn it with the tip on point B, then, put the tip on the intersection of the arc and line AB and then drawn an arc, and done the same for line CB

1. You are correct.

23. He should have drawn the arcs starting with the tip of the compass on point B. After drawing two arcs, he should put the tip of the arm on the intersection of the arc and line AB and then draw another arc and do the same for line CB.