IX S.A -1 Q7.Prove that an equilateral triangle can be
constructed on any given line segment.Consider the circle drawn by
taking A as centre and radius AB. It is clear that point C lies on
it (as C is the point of the intersection of two circles). Join AC.
Thus, AB and AC are the two radii of the same circle. Hence, they
are equal.Now, consider the circle drawn by taking B as centre and
radius AB. It is clear that point C lies on it as well. Join BC.
Thus, BC and AC are the two radii of the same circle. Hence, an
equilateral triangle can be constructed on any straight line.
If a side of your triangle is[AB]thenAandBare 2 points out of 3
from your triangle. You want then to findCsuch thatABCwould be
equilateral. To do this, just draw the circle of centreAand
radiusAB. Then draw the circle of centreBand radiusAB. The point of
intersection of the circles is the pointC. You then have your
triangle!
Calendar key ring usage:Turn the upper disc, aligning the year
and month you are to seek, then the diagonal direction will show
you the week information of each day in the month. You can know the
week of every day in the range of 2010-2060 Black "S" means
Saturday and red "S" means Sunday. When you seek for January or
February in a leap year, you should be aligning with the red "JAN"
and "FEB"
