(i)Prove that every line segment has one & only one midpoint.
(ii)In the given figure angle 3 space & space angle 4 are exterior angles of quadrilateral ABCD at point B & D & angle A equals angle 2 comma angle C equals angle 1. space P r o v e space t h a t space angle 3 plus angle 4 equals angle 1 plus angle 2

Asked by araima2001 | 13th Sep, 2014, 10:48: AM

Expert Answer:

Show that a line segment has one and only one mid-point.

Proof: Let point R be teh mid point of line segment PQ.
Let if posssible, O be another mid-point of PQ.
rightwards double arrowPO = OQ       ....(1)
But, it is given that R is the mid point of PQ.

rightwards double arrowPR = RQ       ....(2)
Subtracting (1) from (2), We get 

Syntax error from line 1 column 69 to line 1 column 119. Unexpected 'PR'.
Therefore, O and R must coincide.
Thus, every line segment has only one mid-point.

Answered by Mili Hariyani | 14th Sep, 2014, 03:13: AM

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