1)prove that an equilateral triangle can be constructed on any given line segment.

2)prove that medians of an equilateral triangle are equal.

3)the points(other than the origin)for which the abcssica is equal to the ordinate lie in quadrant___________.

Due to paucity of time we are providing you the solution of one of your questions. Try solving other and if you face any difficulty than do get back to us.

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.

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