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  • Line segmants ab and cd bisect each other at o. Join ac and ab. Prove that aoc is equal to bod

Line segmants ab and cd bisect each other at o. Join ac and ab. Prove that aoc is equal to bod

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By;linear;pair\*angle AOC+angle AOD=180^circ;;;;;;;;...eq(1)\* angle AOD+angle BOD=180^circ;;;;;;...eq(2)\*from;eq(1);and ;eq(2)\*angle AOC+angle AOD=angle AOD+angle BOD\*Rightarrow angle AOC=angle BOD\* Similarly;(angle AOD=angle COB)\* herefore angle AOC=angle BOD\* Line;segments;AB;and;CD; bisect;each;other;at;O.;So,;O;is;midpoint;of;CD;and;AB\* Rightarrow AO=OB;and;CO=OD\*Now,;In; riangle AOC;and; riangle BOD\*Rightarrow OA=OB\*Rightarrow OC=OD\*Rightarrow angle AOC=angle BOD;;;;;;(vertically;opposite;angle)\*So,;by; SAS;property;of;congruency;triangles;are;congruent\* herefore riangle AOCcong riangle BOD

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Deependra Verma

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