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  • BM and CN are perpendiculars to a line passing through the vertex A of a triangle ABC.If L is the mid-point of BC,prove that LM=LN

BM and CN are perpendiculars to a line passing through the vertex A of a triangle ABC.If L is the mid-point of BC,prove that LM=LN

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If;a;transversal;make;equal;intercepts;on;three;or;more;parallel; lines,\*then;any;other;transversal;intersecting;them;will;also;make; equal;intercepts.\*BM perp MN,;CN perp NM ;and;OL perp MN.\*O;is;the;point;where;perpendicular;from;L;meets;MN\* herefore BM;||;CN;||OL\* Now,;BM || OL || CN ;and;BC;is;the; transversal;making;equal;intercepts;i.e.,;BL = LC\* herefore The; transversal;MN;will;also;make;equal;intercepts.\*Rightarrow OM=ON \* In; riangle LMO ;and; riangle LNO,\*OM = ON \*angle LOM = angle LON;;; (OL;is;perpendicular;to;BC)\*OL=OL;;;;;;;;;;;;;;(Common;line)\*Rightarrow herefore riangle LOM cong riangle LON;by;SAS;property\* Rightarrow herefore LM=LN;;(By;CPCT)\*

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Deependra Verma

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