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Name: __________________________ |
Sketchpad Lab III
1. Open a new sketch.
2. Place two points on your sketch and CONSTRUCT the segment joining them.
3. CONSTRUCT and label the midpoint C. Label the endpoints A and B.
4. Construct the perpendicular bisector of AB.
5. Use CONSTRUCT, POINT ON OBJECT, to place another point on the perpendicular bisector. Label it D.
6. Measure the lengths AD and BD. Move point D to a different location on the perpendicular bisector.
7. Repeat #6 until you have the data you need to complete this table of lengths:
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1st location |
2nd location |
3rd location |
4th location |
5th location |
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AD |
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BD |
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8. Close and do not save your sketch.
9. Open a new sketch.
10. Place two circles with different length radii on your sketch so that they intersect in two points. Use CONSTRUCT POINT AT INTERSECTION to show the points of intersection.
11. Construct the segment joining the centers of the circles.
12. Construct the segment joining the two points of intersection of the circles.
13. Construct the point of intersection of these two segments.
14. Label your points as I have in my sketch, and measure the lengths I have measured.
15. Which pairs of line segments remain congruent to each other, even when you change the sizes of the circles?
16. Use your work on this sketch to fill in the blanks correctly:
_________ is the perpendicular bisector of _________.
17. Raise your hand so that I can check your work. Then close and do not save your sketch.
18. Open a new sketch.
19. Place four points on the sketch so that no three of them are collinear.
20. Construct the six line segments connecting all possible pairs of these points.
21. Two of these line segments should intersect. Construct the point of intersection.
22. Label your drawing as I have labeled mine.
23. Measure the eight line segments and Ð QPR , as I have.
24. Now, move points around until P is the midpoint of sRS but not the midpoint of sQT,
and mÐ QPR = 90˚.
Record these lengths: QR = _____, RT = ______, TS = _______, SQ = ______
25. Now, move points around until P is the midpoint of sQT but not the midpoint of sRS,
and mÐ QPR = 90˚.
Record these lengths: QR = _____, RT = ______, TS = _______, SQ = ______
26. Now, move points around until P is the midpoint of sQT and the midpoint of RS,
and mÐ QPR = 90˚.
Record these lengths: QR = _____, RT = ______, TS = _______, SQ = ______
27. Now, move points around until P is neither the midpoint of sQT nor the midpoint of sRS,
and mÐ QPR = 90˚.
Record these lengths: QR = _____, RT = ______, TS = _______, SQ = ______
28. Write your observations and at least two conjectures.