In Question 4point C Is Called A Mid Point Of The Line Segment Ab।prove That Every Line Segment Has
In Question 4 Point C Is Called A Mid Point Of Line Segment Ab Prove In question 4, point c is called a mid point of line segment ab. prove that every line segment has one and only one mid point. solution: we know that the things which coincide with one another are equal to one another. let us consider that line segment ab has two midpoints ‘c’ and ‘d’ as shown in the figure below. From equations (1) and (2), we get : ⇒ ac = ad. ⇒ c has to coincide with d for ac to be equal to ad. according to euclid's axiom 4: things which coincide with one another are equal to one another. hence, proved that a line segment has only one midpoint. answered by. 2 likes. in question 4, point c is called a mid point of line segment ab.
Point C Is Called A Mid Point Of Line Segment Ab Prove That Every Line Given: c is the mid point of ab such that ac = bc. to prove: ab has one and only mid point c. proof: suppose c and c' be the two mid points of ab. therefore ac = ab 2 and ac' = ab 2 => ac = ac' which is possible only when c and c' coincide => points c and c' are identical. hence, every line segment has one and only one mid point c. Ex 5.1, 5 in the above question, point c is called a mid point of line segment ab, prove that every line segment has one and only one mid point. in previous question, c was mid point of ab. Step by step video & image solution for in question 4, point 'c' is called a midpoint of line segment ab. prove that every line segment has one and only one mid point. by maths experts to help you in doubts & scoring excellent marks in class 9 exams. Let c and d are two mid points of line segment ab. according to question 4, we have, ac = 1 2 ab and ad = 1 2 ab ⇒ ac = ad [things which are equal to the same thing are equal to one another] it is possible only if c and d coincide with each other. hence, the mid point c is unique.
In Question 4 Point C Is Called A Mid Point Of Line Segment Ab Prove Step by step video & image solution for in question 4, point 'c' is called a midpoint of line segment ab. prove that every line segment has one and only one mid point. by maths experts to help you in doubts & scoring excellent marks in class 9 exams. Let c and d are two mid points of line segment ab. according to question 4, we have, ac = 1 2 ab and ad = 1 2 ab ⇒ ac = ad [things which are equal to the same thing are equal to one another] it is possible only if c and d coincide with each other. hence, the mid point c is unique. Let there be two such mid points c and d. then from above theorem ac = 1 2 ab and ad = 1 2 ab ∴ ac = ad but this is possible only if d coincides with c. therefore c is the unique mid point. proved. In the above question, point c is called a mid point of line segment ab, prove that every line segment has one and only one mid point.
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